
Time bar (total: 15.3s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.8s | 26 833× | 0 | invalid |
| 648.0ms | 5 461× | 0 | valid |
| 579.0ms | 2 795× | 1 | valid |
const: 920.0ms (25.8% of total)ival-tan: 696.0ms (19.5% of total)ival-mult: 307.0ms (8.6% of total)ival-fabs: 298.0ms (8.4% of total)ival-<: 272.0ms (7.6% of total)ival-sub: 271.0ms (7.6% of total)ival-<=: 270.0ms (7.6% of total)ival-add: 264.0ms (7.4% of total)ival-and: 117.0ms (3.3% of total)adjust: 86.0ms (2.4% of total)exact: 49.0ms (1.4% of total)ival-assert: 14.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 229 | 3 | (-2.384716976710138e-116 1.374287835806686e-118) | 3 | (-1.240971978149772e-7 3.3688265636766026e-9) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2 | 0 | - | 0 | - | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | cancellation | 229 | 9 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 2 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 226 | 3 |
| - | 3 | 24 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 226 | 3 | 0 |
| - | 3 | 6 | 18 |
| number | freq |
|---|---|
| 0 | 27 |
| 1 | 227 |
| 2 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 19.0ms | 160× | 1 | valid |
| 19.0ms | 348× | 0 | valid |
| 1.0ms | 4× | 2 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-tan: 11.0ms (47% of total)adjust: 6.0ms (25.6% of total)ival-add: 3.0ms (12.8% of total)ival-sub: 3.0ms (12.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
| 102× | sub-neg |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 68× | cancel-sign-sub-inv |
| 64× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 36× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(tan.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x eps) | |
| accuracy | 0 | (tan.f64 x) | |
| accuracy | 0.11500996406283642 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 23.91945418442801 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | 174× | 0 | valid |
| 8.0ms | 80× | 1 | valid |
| 0.0ms | 2× | 2 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 4.0ms (39.3% of total)adjust: 2.0ms (19.6% of total)ival-add: 2.0ms (19.6% of total)ival-sub: 2.0ms (19.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ()) |
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt x (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | eps | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 3.0ms | eps | @ | inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 2.0ms | x | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | eps | @ | -inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | x | @ | -inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1× | egg-herbie |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 5 316× | lower-*.f64 |
| 5 316× | lower-*.f32 |
| 2 664× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5964 | 1242 |
| 0 | 8538 | 1195 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
| Outputs |
|---|
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
x |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 x eps) |
(* eps (+ 1 (/ x eps))) |
(+.f64 x eps) |
(* eps (+ 1 (/ x eps))) |
(+.f64 x eps) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 x eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 x eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 x eps) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
eps |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 x eps) |
(* x (+ 1 (/ eps x))) |
(+.f64 x eps) |
(* x (+ 1 (/ eps x))) |
(+.f64 x eps) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 x eps) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 x eps) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 x eps) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
| 4 404× | lower-*.f64 |
| 4 404× | lower-*.f32 |
| 3 318× | lower-/.f64 |
| 3 318× | lower-/.f32 |
| 3 264× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(tan.f64 x) |
| Outputs |
|---|
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Compiled 8 346 to 1 016 computations (87.8% saved)
16 alts after pruning (15 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 321 | 15 | 336 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 321 | 16 | 337 |
| Status | Accuracy | Program |
|---|---|---|
| 62.7% | (fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) | |
| 62.4% | (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) | |
| 62.7% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ▶ | 62.4% | (fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
| 62.5% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 62.5% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) | |
| ▶ | 62.6% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
| ▶ | 61.9% | (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
| 38.3% | (-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) | |
| 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.1% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| ▶ | 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
Compiled 859 to 406 computations (52.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 eps) | |
| cost-diff | 0 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| cost-diff | 0 | (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| cost-diff | 0 | (neg.f64 (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 192 | (fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) | |
| cost-diff | 5888 | (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) | |
| cost-diff | 0 | (tan.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) | |
| cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) | |
| cost-diff | 7168 | (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) | |
| cost-diff | 0 | (cos.f64 eps) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| cost-diff | 192 | (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| cost-diff | 26816 | (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) | |
| cost-diff | 79872 | (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| 28 628× | lower-fma.f32 |
| 28 608× | lower-fma.f64 |
| 3 966× | lower-+.f32 |
| 3 960× | lower-+.f64 |
| 3 542× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 1165 |
| 0 | 111 | 1173 |
| 1 | 177 | 1015 |
| 2 | 367 | 991 |
| 3 | 1282 | 850 |
| 4 | 6286 | 850 |
| 0 | 8050 | 831 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) |
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
#s(literal -1/6 binary64) |
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 1/6 binary64) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
#s(literal 1/3 binary64) |
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) |
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
eps |
(cos.f64 eps) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1 binary64) |
(tan.f64 x) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
x |
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
#s(literal -1 binary64) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) |
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) |
(fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)))) |
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(+.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(literal -1/6 binary64) |
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 1/6 binary64) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) |
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
(*.f64 (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))) |
#s(literal 1/3 binary64) |
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) |
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
eps |
(cos.f64 eps) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(tan.f64 (+.f64 eps x)) |
#s(literal 1 binary64) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1 binary64) |
(tan.f64 x) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(sin.f64 x) |
x |
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
#s(literal -1 binary64) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) (tan.f64 x)) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (neg.f64 (tan.f64 eps)) | |
| accuracy | 0.0078125 | (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) | |
| accuracy | 0.01953125 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 23.91945418442801 | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| accuracy | 0 | (neg.f64 (cos.f64 x)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.11500996406283642 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 23.916660960492692 | (fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) | |
| accuracy | 0.11500996406283642 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 0.25390625 | (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) | |
| accuracy | 0.265625 | (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) | |
| accuracy | 23.91945418442801 | (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) | |
| accuracy | 0 | (sin.f64 eps) | |
| accuracy | 0 | (cos.f64 eps) | |
| accuracy | 0.00390625 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| accuracy | 1.513301546439125 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| accuracy | 0.037441259768442016 | (pow.f64 (sin.f64 x) #s(literal 3 binary64)) | |
| accuracy | 0.14453125 | (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| accuracy | 0.2890625 | (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) | |
| accuracy | 0.994472509768442 | (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
| 107.0ms | 169× | 0 | valid |
| 94.0ms | 85× | 1 | valid |
| 3.0ms | 2× | 2 | valid |
Compiled 1 071 to 68 computations (93.7% saved)
const: 39.0ms (22.9% of total)ival-pow: 23.0ms (13.5% of total)ival-mult: 23.0ms (13.5% of total)ival-add: 20.0ms (11.7% of total)ival-div: 17.0ms (10% of total)adjust: 14.0ms (8.2% of total)ival-tan: 9.0ms (5.3% of total)ival-sub: 7.0ms (4.1% of total)ival-pow2: 6.0ms (3.5% of total)ival-cos: 4.0ms (2.3% of total)ival-sin: 4.0ms (2.3% of total)ival-neg: 3.0ms (1.8% of total)exact: 1.0ms (0.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
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#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ()) |
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#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) #<representation binary64>) () ()) |
#s(alt (/.f64 (sin.f64 eps) (cos.f64 eps)) (patch (/.f64 (sin.f64 eps) (cos.f64 eps)) #<representation binary64>) () ()) |
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ()) |
#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (tan.f64 (+.f64 eps x)) (patch (tan.f64 (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (patch (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) (patch (fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) #<representation binary64>) () ()) |
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ()) |
#s(alt (neg.f64 (cos.f64 x)) (patch (neg.f64 (cos.f64 x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) (patch (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (patch (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (tan.f64 eps) (tan.f64 x)) (patch (+.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (tan.f64 eps) (patch (tan.f64 eps) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (patch (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ()) |
#s(alt (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #<representation binary64>) () ()) |
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ()) |
#s(alt (neg.f64 (tan.f64 eps)) (patch (neg.f64 (tan.f64 eps)) #<representation binary64>) () ()) |
| Outputs |
|---|
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#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (patch (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (patch (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ()) |
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 21.0ms | x | @ | inf | ((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (tan (+ eps x)) -1)) (- (/ 1 (pow (tan (+ eps x)) -1)) (tan x)) (pow (tan (+ eps x)) -1) (tan (+ eps x)) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (cos x) (neg (tan eps))) |
| 14.0ms | x | @ | -inf | ((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (tan (+ eps x)) -1)) (- (/ 1 (pow (tan (+ eps x)) -1)) (tan x)) (pow (tan (+ eps x)) -1) (tan (+ eps x)) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (cos x) (neg (tan eps))) |
| 12.0ms | eps | @ | inf | ((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (tan (+ eps x)) -1)) (- (/ 1 (pow (tan (+ eps x)) -1)) (tan x)) (pow (tan (+ eps x)) -1) (tan (+ eps x)) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (cos x) (neg (tan eps))) |
| 11.0ms | eps | @ | 0 | ((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (tan (+ eps x)) -1)) (- (/ 1 (pow (tan (+ eps x)) -1)) (tan x)) (pow (tan (+ eps x)) -1) (tan (+ eps x)) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (cos x) (neg (tan eps))) |
| 9.0ms | x | @ | 0 | ((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (tan (+ eps x)) -1)) (- (/ 1 (pow (tan (+ eps x)) -1)) (tan x)) (pow (tan (+ eps x)) -1) (tan (+ eps x)) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (cos x) (neg (tan eps))) |
| 1× | egg-herbie |
| 8 188× | lower-fma.f64 |
| 8 188× | lower-fma.f32 |
| 6 266× | lower-*.f64 |
| 6 266× | lower-*.f32 |
| 4 462× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 660 | 12007 |
| 1 | 2059 | 11579 |
| 2 | 7473 | 11518 |
| 0 | 8036 | 11106 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
1 |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (cos x) (sin x)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1 eps) |
(* eps (- (* -1/3 (pow eps 2)) 1)) |
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1)) |
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1)) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
(* -1 (/ (sin eps) (cos eps))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x)))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
-1/2 |
(- (* -1/3 (pow x 2)) 1/2) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
-1 |
(- (* 1/2 (pow x 2)) 1) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(* 1/3 x) |
(* x (+ 1/3 (* 4/9 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2)))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(pow x 3) |
(* (pow x 3) (+ 1 (* -1/2 (pow x 2)))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2)))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2)))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
| Outputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) |
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(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ eps (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps)) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* -1 eps) |
(neg.f64 eps) |
(* eps (- (* -1/3 (pow eps 2)) 1)) |
(*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)) eps) |
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1)) |
(*.f64 (fma.f64 (fma.f64 #s(literal -2/15 binary64) (*.f64 eps eps) #s(literal -1/3 binary64)) (*.f64 eps eps) #s(literal -1 binary64)) eps) |
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1)) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (*.f64 eps eps) #s(literal -2/15 binary64)) (*.f64 eps eps) #s(literal -1/3 binary64)) (*.f64 eps eps) #s(literal -1 binary64)) eps) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) eps) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))) |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
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(/ (sin eps) (cos eps)) |
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(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
(* -1 (/ (sin eps) (cos eps))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
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(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
(* -1 (/ (sin eps) (cos eps))) |
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(* -1 (/ (sin eps) (cos eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) |
1/3 |
#s(literal 1/3 binary64) |
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(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* -1/3 (pow x 2)) 1/2) |
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) |
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) |
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1/3 |
#s(literal 1/3 binary64) |
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(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/9 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
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(/ (sin eps) (cos eps)) |
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(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
| 5 604× | lower-fma.f32 |
| 5 584× | lower-fma.f64 |
| 5 116× | lower-*.f32 |
| 5 114× | lower-*.f64 |
| 2 412× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 615 |
| 0 | 111 | 581 |
| 1 | 515 | 426 |
| 2 | 5117 | 426 |
| 0 | 8467 | 398 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
(cos.f64 eps) |
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(tan.f64 (+.f64 eps x)) |
(pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
(neg.f64 (cos.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(cos.f64 x) |
(neg.f64 (tan.f64 eps)) |
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Compiled 155 178 to 5 975 computations (96.1% saved)
25 alts after pruning (24 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 882 | 17 | 1 899 |
| Fresh | 3 | 7 | 10 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 890 | 25 | 1 915 |
| Status | Accuracy | Program |
|---|---|---|
| 62.7% | (fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) | |
| 62.4% | (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) | |
| ▶ | 62.7% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| 62.4% | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) | |
| 61.6% | (fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) | |
| 61.7% | (/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) | |
| 62.5% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 62.5% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) | |
| ▶ | 31.2% | (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
| 62.5% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ▶ | 61.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
| 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.1% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 57.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) eps eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) | |
| 99.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| ▶ | 5.4% | #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 1 389 to 650 computations (53.2% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 eps) | |
| cost-diff | 0 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| cost-diff | 0 | (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | (tan.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) | |
| cost-diff | 0 | (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) | |
| cost-diff | 0 | (tan.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) | |
| cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| cost-diff | 1408 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) | |
| cost-diff | 0 | #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) | |
| cost-diff | 256 | (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) | |
| cost-diff | 6144 | (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) | |
| cost-diff | 6720 | (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) | |
| cost-diff | 58432 | (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) |
| 14 592× | lower-fma.f32 |
| 14 570× | lower-fma.f64 |
| 4 382× | lower-+.f32 |
| 4 378× | lower-+.f64 |
| 3 726× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 793 |
| 0 | 108 | 785 |
| 1 | 192 | 771 |
| 2 | 488 | 665 |
| 3 | 1612 | 664 |
| 4 | 5258 | 660 |
| 0 | 8570 | 635 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) |
eps |
(fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) |
(tan.f64 x) |
x |
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) |
(pow.f64 (cos.f64 x) #s(literal -2 binary64)) |
(cos.f64 x) |
#s(literal -2 binary64) |
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(sin.f64 x) |
#s(literal 4 binary64) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) |
#s(literal -1/6 binary64) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
#s(literal -1/2 binary64) |
(*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
#s(literal 1/3 binary64) |
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(tan.f64 x) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1/2 binary64) |
#s(literal -2 binary64) |
(tan.f64 x) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
#s(literal 2 binary64) |
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (sin.f64 x)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (sin.f64 x)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (sin.f64 x)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (sin.f64 x)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) |
(fma.f64 (/.f64 eps (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (sin.f64 x)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) |
eps |
(fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (tan.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (tan.f64 x))) |
(tan.f64 x) |
x |
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) |
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) |
(pow.f64 (cos.f64 x) #s(literal -2 binary64)) |
(cos.f64 x) |
#s(literal -2 binary64) |
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(sin.f64 x) |
#s(literal 4 binary64) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) |
(fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) |
#s(literal -1/6 binary64) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
#s(literal -1/2 binary64) |
(*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
(*.f64 (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
#s(literal 1/3 binary64) |
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) |
(tan.f64 (+.f64 eps x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(tan.f64 x) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1/2 binary64) |
#s(literal -2 binary64) |
(tan.f64 x) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
#s(literal 2 binary64) |
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 x)) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (*.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 0.015625 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 0.07945253907376808 | (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) | |
| accuracy | 12.794501147032713 | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.05078125 | (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) | |
| accuracy | 0.10719746406283642 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 0.29201127930532605 | (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) | |
| accuracy | 12.815801801500148 | (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) | |
| accuracy | 0.10719746406283642 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 0.13671875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) | |
| accuracy | 0.15625 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) | |
| accuracy | 12.815801801500148 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| accuracy | 31.704012359988923 | #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) | |
| accuracy | 0.015625 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.09765625 | (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.14453125 | (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) | |
| accuracy | 0.515625 | (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) |
| 82.0ms | 122× | 0 | invalid |
| 54.0ms | 48× | 1 | valid |
| 39.0ms | 84× | 0 | valid |
| 10.0ms | 2× | 2 | valid |
Compiled 758 to 67 computations (91.2% saved)
ival-mult: 40.0ms (26.8% of total)ival-pow: 24.0ms (16.1% of total)ival-add: 18.0ms (12.1% of total)ival-tan: 15.0ms (10.1% of total)const: 10.0ms (6.7% of total)adjust: 9.0ms (6% of total)ival-pow2: 8.0ms (5.4% of total)ival-div: 7.0ms (4.7% of total)ival-sub: 6.0ms (4% of total)ival-neg: 5.0ms (3.4% of total)ival-cos: 2.0ms (1.3% of total)ival-sin: 2.0ms (1.3% of total)exact: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) (patch (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (patch (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (patch (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) (patch (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #<representation binary64>) () ()) |
#s(alt (tan.f64 (+.f64 eps x)) (patch (tan.f64 (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) (patch (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (patch (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) (patch (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (patch (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) #<representation binary64>) () ()) |
#s(alt (+.f64 (tan.f64 eps) (tan.f64 x)) (patch (+.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (tan.f64 eps) (patch (tan.f64 eps) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) (patch (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (tan.f64 eps) (tan.f64 x)) (patch (*.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ()) |
| Outputs |
|---|
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#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) (patch (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) (patch (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) (patch (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin x) (cos x)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) (patch (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) #<representation binary64>) () ())) ()) |
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | x | @ | inf | ((+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (/ 1 (tan (+ eps x)))) (- (/ 1 (/ 1 (tan (+ eps x)))) (tan x)) (/ 1 (tan (+ eps x))) (tan (+ eps x)) (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (pow (pow (tan (+ eps x)) -1/2) -2) (pow (tan (+ eps x)) -1/2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (sin x) 4) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 12.0ms | eps | @ | -inf | ((+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (/ 1 (tan (+ eps x)))) (- (/ 1 (/ 1 (tan (+ eps x)))) (tan x)) (/ 1 (tan (+ eps x))) (tan (+ eps x)) (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (pow (pow (tan (+ eps x)) -1/2) -2) (pow (tan (+ eps x)) -1/2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (sin x) 4) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 11.0ms | x | @ | -inf | ((+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (/ 1 (tan (+ eps x)))) (- (/ 1 (/ 1 (tan (+ eps x)))) (tan x)) (/ 1 (tan (+ eps x))) (tan (+ eps x)) (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (pow (pow (tan (+ eps x)) -1/2) -2) (pow (tan (+ eps x)) -1/2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (sin x) 4) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 8.0ms | eps | @ | inf | ((+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (/ 1 (tan (+ eps x)))) (- (/ 1 (/ 1 (tan (+ eps x)))) (tan x)) (/ 1 (tan (+ eps x))) (tan (+ eps x)) (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (pow (pow (tan (+ eps x)) -1/2) -2) (pow (tan (+ eps x)) -1/2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (sin x) 4) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 8.0ms | eps | @ | 0 | ((+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (/ 1 (tan (+ eps x)))) (- (/ 1 (/ 1 (tan (+ eps x)))) (tan x)) (/ 1 (tan (+ eps x))) (tan (+ eps x)) (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (pow (pow (tan (+ eps x)) -1/2) -2) (pow (tan (+ eps x)) -1/2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (sin x) 4) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 1× | egg-herbie |
| 10 514× | lower-fma.f64 |
| 10 514× | lower-fma.f32 |
| 7 830× | lower-*.f64 |
| 7 830× | lower-*.f32 |
| 5 150× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 733 | 13752 |
| 1 | 2452 | 13231 |
| 0 | 8285 | 12799 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (cos x) (sin x)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(sqrt (/ (cos x) (sin x))) |
(+ (sqrt (/ (cos x) (sin x))) (* -1/2 (* (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sqrt (/ (pow (cos x) 3) (pow (sin x) 3)))))) |
(+ (sqrt (/ (cos x) (sin x))) (* eps (+ (* -1/2 (* (sqrt (/ (pow (cos x) 3) (pow (sin x) 3))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1/2 (* (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* 1/4 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (sqrt (/ (sin x) (cos x)))))))) |
(+ (sqrt (/ (cos x) (sin x))) (* eps (+ (* -1/2 (* (sqrt (/ (pow (cos x) 3) (pow (sin x) 3))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* eps (+ (* -1/2 (* (sqrt (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* 1/4 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))))) (* -1/2 (* (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* 1/4 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))))))) (sqrt (/ (sin x) (cos x)))))))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(sqrt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(sqrt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(sqrt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(sqrt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x)))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
(* 2/3 x) |
(* x (+ 2/3 (* 17/9 (pow x 2)))) |
(* x (+ 2/3 (* (pow x 2) (+ 17/9 (* 124/45 (pow x 2)))))) |
(* x (+ 2/3 (* (pow x 2) (+ 17/9 (* (pow x 2) (+ 124/45 (* 2764/945 (pow x 2)))))))) |
x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(* 1/3 x) |
(* x (+ 1/3 (* 4/9 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
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(/ (sin eps) (cos eps)) |
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (cos eps) (sin eps)) |
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(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sqrt (/ (cos eps) (sin eps))) |
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(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
1/3 |
(+ 1/3 (* 1/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 1/3 (* 2/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/9 (* 17/135 (pow x 2))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) |
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(/ (* x (sin eps)) (cos eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
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(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(sqrt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(sqrt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(sqrt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(sqrt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
| Outputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ eps (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
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(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (fma.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ eps (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) eps) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 62/315 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps)) |
(/ (* eps (sin x)) (cos x)) |
(/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))) eps) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
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(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
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(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
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(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
(sqrt (/ (cos (+ eps x)) (sin (+ eps x)))) |
(sqrt.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
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1/3 |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) |
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps))) |
| 7 218× | lower-fma.f32 |
| 7 198× | lower-fma.f64 |
| 4 716× | lower-*.f32 |
| 4 712× | lower-*.f64 |
| 2 538× | lower-pow.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 374 |
| 0 | 100 | 358 |
| 1 | 466 | 346 |
| 2 | 4130 | 306 |
| 0 | 8275 | 306 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) |
(fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)) |
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
| Outputs |
|---|
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Compiled 68 223 to 4 372 computations (93.6% saved)
26 alts after pruning (21 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 314 | 7 | 1 321 |
| Fresh | 5 | 14 | 19 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 320 | 26 | 1 346 |
| Status | Accuracy | Program |
|---|---|---|
| 62.7% | (fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) | |
| ▶ | 62.4% | (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
| ✓ | 62.7% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| 62.4% | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) | |
| ▶ | 61.6% | (fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
| 61.7% | (/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) | |
| 62.5% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 62.5% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) | |
| ✓ | 31.2% | (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
| 62.5% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ✓ | 61.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
| 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.1% | #s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) | |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(approx (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (*.f64 #s(literal 2/3 binary64) x)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| ▶ | 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 57.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) eps eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) | |
| 99.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) | |
| ▶ | 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| ✓ | 5.4% | #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 1 330 to 651 computations (51.1% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| cost-diff | 6144 | (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) | |
| cost-diff | 12608 | (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | (+.f64 eps x) | |
| cost-diff | 0 | (cos.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) | |
| cost-diff | 6080 | (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) | |
| cost-diff | 0 | #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) | |
| cost-diff | 0 | (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) | |
| cost-diff | 0 | (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) | |
| cost-diff | 512 | (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) | |
| cost-diff | 12608 | (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 13184 | (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 25472 | (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
| 16 704× | lower-fma.f32 |
| 16 674× | lower-fma.f64 |
| 3 990× | lower-+.f32 |
| 3 984× | lower-+.f64 |
| 3 868× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 111 | 1662 |
| 0 | 174 | 1656 |
| 1 | 331 | 1562 |
| 2 | 857 | 1423 |
| 3 | 3251 | 1230 |
| 0 | 8129 | 1154 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) |
(+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
#s(literal 1/3 binary64) |
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
#s(literal -1/3 binary64) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sin.f64 x) |
(/.f64 #s(literal 1/3 binary64) (cos.f64 x)) |
(cos.f64 x) |
eps |
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps) |
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
x |
#s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) |
(fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
#s(literal -5/24 binary64) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal -1 binary64) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1 binary64) |
(sin.f64 (+.f64 eps x)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
#s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
eps |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(sin.f64 x) |
x |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(cos.f64 x) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps) eps (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(*.f64 (fma.f64 (*.f64 (fma.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps) eps (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) |
(fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) |
(fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (+.f64 (tan.f64 x) (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 5 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) |
(+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(+.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)) |
(+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
#s(literal -1/3 binary64) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) |
(*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sin.f64 x) |
(/.f64 #s(literal 1/3 binary64) (cos.f64 x)) |
(cos.f64 x) |
eps |
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps) |
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
x |
#s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) |
#s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) |
(fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -5/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -5/24 binary64) #s(literal -1/2 binary64)) |
#s(literal -5/24 binary64) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal -1 binary64) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal -1 binary64) |
(sin.f64 (+.f64 eps x)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
(fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(*.f64 (fma.f64 (*.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps) |
(fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
#s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
eps |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(sin.f64 x) |
x |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(cos.f64 x) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.02181625976844202 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| accuracy | 0.03125 | (pow.f64 (tan.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.14453125 | (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 1.5846655791862343 | #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) | |
| accuracy | 0.00390625 | (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) | |
| accuracy | 0.07015413533754951 | (sin.f64 (+.f64 eps x)) | |
| accuracy | 0.09641390224715446 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 23.905726014447726 | (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.0078125 | (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) | |
| accuracy | 0.11500996406283642 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 0.8499724925334624 | #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) | |
| accuracy | 23.916660960492692 | (fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) | |
| accuracy | 0 | (*.f64 eps eps) | |
| accuracy | 0.02181625976844202 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) | |
| accuracy | 0.20703125 | (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) | |
| accuracy | 31.651650335864595 | #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) | |
| accuracy | 0.03972626953688403 | (pow.f64 (tan.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.14453125 | (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.1953125 | (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.28515625 | (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) |
| 223.0ms | 87× | 1 | valid |
| 143.0ms | 167× | 0 | valid |
| 4.0ms | 2× | 2 | valid |
Compiled 1 319 to 115 computations (91.3% saved)
ival-mult: 97.0ms (29.9% of total)ival-pow: 65.0ms (20% of total)ival-add: 42.0ms (12.9% of total)ival-div: 28.0ms (8.6% of total)adjust: 24.0ms (7.4% of total)const: 23.0ms (7.1% of total)ival-pow2: 15.0ms (4.6% of total)ival-sin: 9.0ms (2.8% of total)ival-sub: 7.0ms (2.2% of total)ival-tan: 7.0ms (2.2% of total)ival-cos: 5.0ms (1.5% of total)ival-neg: 3.0ms (0.9% of total)exact: 1.0ms (0.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
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#s(alt (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) (patch (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 eps eps) (patch (*.f64 eps eps) #<representation binary64>) () ()) |
#s(alt (tan.f64 (+.f64 eps x)) (patch (tan.f64 (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) (patch #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ()) |
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 28.0ms | eps | @ | 0 | ((+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (pow (neg (cos x)) -1) (+ (* (+ (* -5/24 (* x x)) -1/2) (* x x)) -1) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (tan (+ eps x)) (+ (* -5/24 (* x x)) -1/2) (sin (+ eps x)) (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (pow (tan x) 2)) |
| 15.0ms | x | @ | inf | ((+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (pow (neg (cos x)) -1) (+ (* (+ (* -5/24 (* x x)) -1/2) (* x x)) -1) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (tan (+ eps x)) (+ (* -5/24 (* x x)) -1/2) (sin (+ eps x)) (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (pow (tan x) 2)) |
| 15.0ms | x | @ | -inf | ((+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (pow (neg (cos x)) -1) (+ (* (+ (* -5/24 (* x x)) -1/2) (* x x)) -1) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (tan (+ eps x)) (+ (* -5/24 (* x x)) -1/2) (sin (+ eps x)) (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (pow (tan x) 2)) |
| 8.0ms | eps | @ | -inf | ((+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (pow (neg (cos x)) -1) (+ (* (+ (* -5/24 (* x x)) -1/2) (* x x)) -1) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (tan (+ eps x)) (+ (* -5/24 (* x x)) -1/2) (sin (+ eps x)) (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (pow (tan x) 2)) |
| 8.0ms | eps | @ | inf | ((+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (pow (neg (cos x)) -1) (+ (* (+ (* -5/24 (* x x)) -1/2) (* x x)) -1) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) eps) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) eps) (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (tan (+ eps x)) (+ (* -5/24 (* x x)) -1/2) (sin (+ eps x)) (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (pow (tan x) 2)) |
| 1× | egg-herbie |
| 10 120× | lower-fma.f64 |
| 10 120× | lower-fma.f32 |
| 6 190× | lower-*.f64 |
| 6 190× | lower-*.f32 |
| 5 880× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 811 | 22874 |
| 1 | 2762 | 22538 |
| 0 | 8241 | 21808 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ 1 (cos x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* (pow eps 4) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps)) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps))) eps)) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x)))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(* 2/3 x) |
(* x (+ 2/3 (* 17/9 (pow x 2)))) |
(* x (+ 2/3 (* (pow x 2) (+ 17/9 (* 124/45 (pow x 2)))))) |
(* x (+ 2/3 (* (pow x 2) (+ 17/9 (* (pow x 2) (+ 124/45 (* 2764/945 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ 1 (cos eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(* 1/3 x) |
(* x (+ 1/3 (* 4/9 (pow x 2)))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2)))))) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2)))))))) |
(* -1/3 (pow x 2)) |
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3)) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 4/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
-1/2 |
(- (* -5/24 (pow x 2)) 1/2) |
(- (* -5/24 (pow x 2)) 1/2) |
(- (* -5/24 (pow x 2)) 1/2) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x)))) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(* -5/24 (pow x 4)) |
(* -1 (* (pow x 4) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(* (pow x 4) (- (* -1 (/ (+ 1/2 (/ 1 (pow x 2))) (pow x 2))) 5/24)) |
(* (pow x 4) (- (* -1 (/ (+ 1/2 (/ 1 (pow x 2))) (pow x 2))) 5/24)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(/ 1 (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -5/24 (pow x 2)) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
| Outputs |
|---|
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
#s(literal 0 binary64) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ 1 (cos x)) |
(/.f64 #s(literal 1 binary64) (cos.f64 x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
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(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
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(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(pow eps 2) |
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(pow eps 2) |
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(pow eps 2) |
(*.f64 eps eps) |
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(/.f64 (sin.f64 x) (cos.f64 x)) |
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(sin x) |
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(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
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(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(* eps (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(* (pow eps 4) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps (cos.f64 x)) eps)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps (cos.f64 x)) eps)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 4 binary64))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 3 binary64))) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ 1 (cos (+ eps x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
(/ 1 (cos (+ eps x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
(/ 1 (cos (+ eps x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
(/ 1 (cos (+ eps x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 4 binary64))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps) eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) eps)))) (-.f64 (/.f64 #s(literal 1/3 binary64) eps) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps (cos.f64 x)) eps)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps (cos.f64 x)) eps)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 3 binary64))) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps) |
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps) |
(* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps) |
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
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(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)))) |
(* (pow eps 4) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
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(* (pow eps 4) (- (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps)) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (neg.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (sin.f64 x) eps) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (neg.f64 eps)))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps))) eps)) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (/.f64 (neg.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps)))) eps)) (pow.f64 eps #s(literal 4 binary64))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(*.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))) |
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))) |
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(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) |
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
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(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
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(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x (neg.f64 eps)) (neg.f64 eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) |
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (-.f64 (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (+.f64 (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (-.f64 (/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))))) |
(* (pow eps 3) (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 (+.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/3 binary64)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))))) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) |
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1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 (*.f64 #s(literal 2/3 binary64) x) eps #s(literal 1/3 binary64)) |
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1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 4/3 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) |
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(+ eps (* 1/3 (pow eps 3))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
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(* 2/3 x) |
(*.f64 #s(literal 2/3 binary64) x) |
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(* 1/3 (pow eps 2)) |
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x |
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-1 |
#s(literal -1 binary64) |
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-1 |
#s(literal -1 binary64) |
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(/ (sin eps) (cos eps)) |
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(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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(/ 1 (cos eps)) |
(/.f64 #s(literal 1 binary64) (cos.f64 eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(fma.f64 x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
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(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x) (sin.f64 eps)) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps (* 1/3 (pow eps 3))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) eps) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) (fma.f64 #s(literal 4/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(* 1/3 x) |
(*.f64 x #s(literal 1/3 binary64)) |
(* x (+ 1/3 (* 4/9 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 4/9 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 248/945 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 4/9 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* -1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/3 binary64)) |
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) |
(*.f64 (*.f64 (fma.f64 #s(literal -2/9 binary64) (*.f64 x x) #s(literal -1/3 binary64)) x) x) |
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -17/135 binary64) (*.f64 x x) #s(literal -2/9 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) x) x) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -62/945 binary64) (*.f64 x x) #s(literal -17/135 binary64)) (*.f64 x x) #s(literal -2/9 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) x) x) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(pow x 4) |
(pow.f64 x #s(literal 4 binary64)) |
(* (pow x 4) (+ 1 (* 4/3 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 6/5 binary64) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 848/945 binary64) (*.f64 x x) #s(literal 6/5 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 x (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* -5/24 (pow x 2)) 1/2) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* -5/24 (pow x 2)) 1/2) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* -5/24 (pow x 2)) 1/2) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 (*.f64 #s(literal 2/3 binary64) x) eps #s(literal 1/3 binary64)) |
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x)))) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) x) x #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
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(fma.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(* -5/24 (pow x 2)) |
(*.f64 #s(literal -5/24 binary64) (*.f64 x x)) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (neg.f64 x) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 5/24 binary64))) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (neg.f64 x) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 5/24 binary64))) |
(* -1 (* (pow x 2) (+ 5/24 (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (neg.f64 x) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 5/24 binary64))) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
| 6 102× | lower-fma.f32 |
| 6 072× | lower-fma.f64 |
| 4 412× | lower-*.f32 |
| 4 400× | lower-*.f64 |
| 3 070× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 110 | 1298 |
| 0 | 173 | 1277 |
| 1 | 897 | 893 |
| 0 | 9413 | 860 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps) |
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
#s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) |
(fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
(fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))) |
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
(*.f64 eps eps) |
(tan.f64 (+.f64 eps x)) |
(fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(sin.f64 (+.f64 eps x)) |
#s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
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Compiled 128 099 to 8 480 computations (93.4% saved)
30 alts after pruning (23 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 958 | 13 | 1 971 |
| Fresh | 6 | 10 | 16 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 5 | 5 |
| Total | 1 967 | 30 | 1 997 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 62.7% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| 62.4% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) | |
| 62.4% | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) | |
| 62.7% | (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) | |
| ✓ | 61.6% | (fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
| 61.6% | (fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) | |
| 61.3% | (fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) | |
| 62.5% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| ✓ | 31.2% | (-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
| 62.5% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ✓ | 61.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
| 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 62.4% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.1% | #s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) | |
| 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) | |
| ✓ | 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) | |
| 97.6% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| ✓ | 5.4% | #s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 2 574 to 750 computations (70.9% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (*.f64 (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) eps eps)) |
3 calls:
| 16.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 15.0ms | x |
| 13.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(approx (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (*.f64 #s(literal 2/3 binary64) x)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 16.0ms | x |
| 13.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps #s(approx (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3)) (*.f64 #s(literal 2/3 binary64) x)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 13.0ms | eps |
| 11.0ms | x |
| 11.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
3 calls:
| 14.0ms | x |
| 12.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 11.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (-.f64 (neg.f64 (cos.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
3 calls:
| 13.0ms | eps |
| 11.0ms | x |
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
| 99.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 208.0ms | x |
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
| 99.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (pow (pow (tan (+ eps x)) -1/2) -2) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | eps |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
| 99.1% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (*.f64 x x) #s(literal 61/120 binary64)) (*.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal -2 binary64)) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 12.0ms | x |
| 7.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) #s(approx (pow (neg (cos x)) -1) (fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
3 calls:
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
3 calls:
| 4.0ms | x |
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | eps |
| 97.6% | 1 | x |
| 97.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
3 calls:
| 2.0ms | x |
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.4% | 1 | x |
| 5.4% | 1 | eps |
| 5.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
| 28× | *-commutative-binary64-*.f64 |
| 16× | +-commutative-binary64-+.f64 |
| 8× | sub-neg-binary64-neg.f64-+.f64--.f64 |
| 6× | neg-sub0-binary64--.f64-neg.f64 |
| 6× | neg-mul-1-binary64-*.f64-neg.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 177 | 1149 |
| 1 | 199 | 1149 |
| 2 | 209 | 1149 |
| 3 | 215 | 1149 |
| 4 | 219 | 1149 |
| 5 | 220 | 1149 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (*.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (tan.f64 x) (*.f64 (/.f64 #s(literal 1/3 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))) eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (tan.f64 x)) (sin.f64 x))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(literal 1/3 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) #s(literal 1/3 binary64) (fma.f64 (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (+ (- 1/3 (* -1/3 (pow (tan x) 2))) (pow (tan x) 4)) (pow (tan x) 2)) (tan x)) (* (* (+ (* (tan x) (tan x)) 1) (sin x)) (/ 1/3 (cos x)))) (*.f64 #s(literal 2/3 binary64) x)) eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* eps (+ (* (tan x) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (* (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)) 1/3))) (+ (* (pow (cos x) -2) (+ (* (pow (cos x) -2) (pow (sin x) 4)) (pow (sin x) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) #s(literal 1/3 binary64)) eps (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (*.f64 (fma.f64 #s(literal 5/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) |
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64)) |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 10 514× | lower-fma.f64 |
| 10 514× | lower-fma.f32 |
| 10 120× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 0 | 811 | 22874 |
| 1 | 2762 | 22538 |
| 0 | 8241 | 21808 |
| 0 | 56 | 374 |
| 0 | 100 | 358 |
| 1 | 466 | 346 |
| 2 | 4130 | 306 |
| 0 | 8275 | 306 |
| 0 | 59 | 615 |
| 0 | 111 | 581 |
| 1 | 515 | 426 |
| 2 | 5117 | 426 |
| 0 | 8467 | 398 |
| 0 | 733 | 13752 |
| 1 | 2452 | 13231 |
| 0 | 8285 | 12799 |
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5964 | 1242 |
| 0 | 8538 | 1195 |
| 0 | 660 | 12007 |
| 1 | 2059 | 11579 |
| 2 | 7473 | 11518 |
| 0 | 8036 | 11106 |
| 0 | 110 | 1298 |
| 0 | 173 | 1277 |
| 1 | 897 | 893 |
| 0 | 9413 | 860 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 686 to 286 computations (58.3% saved)
Compiled 770 to 234 computations (69.6% saved)
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