
Time bar (total: 16.0s)
| 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 | 25 822× | 0 | invalid |
| 854.0ms | 2 817× | 1 | valid |
| 693.0ms | 5 439× | 0 | valid |
ival-tan: 817.0ms (24.7% of total)const: 661.0ms (20% of total)ival-sub: 342.0ms (10.4% of total)ival-<: 330.0ms (10% of total)ival-mult: 247.0ms (7.5% of total)ival-<=: 240.0ms (7.3% of total)ival-add: 208.0ms (6.3% of total)ival-fabs: 200.0ms (6.1% of total)ival-and: 100.0ms (3% of total)adjust: 97.0ms (2.9% of total)exact: 46.0ms (1.4% of total)ival-assert: 12.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 217 | 2 | (-1.9060605947552036e-28 2.591154366978387e-31) | 4 | (9.92110454147757e-119 1.1447745047959546e-120) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | cancellation | 215 | 12 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 213 | 4 |
| - | 2 | 37 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 213 | 4 | 0 |
| - | 2 | 8 | 29 |
| number | freq |
|---|---|
| 0 | 41 |
| 1 | 215 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 21.0ms | 178× | 1 | valid |
| 16.0ms | 332× | 0 | valid |
| 7.0ms | 2× | 3 | valid |
Compiled 49 to 22 computations (55.1% saved)
ival-tan: 19.0ms (65% of total)adjust: 4.0ms (13.7% of total)ival-add: 3.0ms (10.3% of total)ival-sub: 3.0ms (10.3% 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)) |
Compiled 9 to 6 computations (33.3% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 6 computations (33.3% 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)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
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 | 0.0234375 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 24.126973597640735 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 23.0ms | 166× | 0 | valid |
| 11.0ms | 89× | 1 | valid |
| 4.0ms | 1× | 3 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 22.0ms (73.3% of total)adjust: 4.0ms (13.3% of total)ival-add: 2.0ms (6.7% of total)ival-sub: 2.0ms (6.7% 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 (/ (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 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 (* -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 (* 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 (+ 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 (- 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 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 (/ (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 (/ (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 (/ (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 (/ (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 (/ (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 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 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 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 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 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 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 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 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 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>) () ())) ()) |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | eps | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 2.0ms | eps | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | -inf | (- (tan (+ 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 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (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 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 (* -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 (- 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 (+ 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 (- 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)) |
(+ (* 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 x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps 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)) |
(+ (* 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 (+ 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 (* -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 |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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 x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
| Outputs |
|---|
(/ (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (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 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (/.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 (- (* -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 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.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))) (+.f64 #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))) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 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)))) (/.f64 (sin.f64 eps) (cos.f64 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 (* -1 x))) (cos (- eps (* -1 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 (* -1 x))) (cos (- eps (* -1 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 (* -1 x))) (cos (- eps (* -1 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 (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* 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 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) 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 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) 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 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 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 2 binary64)) (/.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 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 (- 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))) |
(/ (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))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x)) |
(+ (* 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 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (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))))) (/.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 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.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 (+.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) (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)))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (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))))) (/.f64 (sin.f64 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 (* -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))) |
(/ (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))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (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))))) (/ (sin x) (cos x))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (+.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 (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 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (+.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 (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 (- 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))) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) 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 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 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 |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
(+.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(+.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))) |
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(-.f64 (/.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))) |
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x)) |
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))) |
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(fma.f64 (tan.f64 x) #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
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(/.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (-.f64 x eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))) |
(tan.f64 x) |
(neg.f64 (neg.f64 (tan.f64 x))) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(*.f64 #s(literal 1 binary64) (tan.f64 x)) |
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) |
Compiled 8 701 to 985 computations (88.7% saved)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 318 | 18 | 336 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 318 | 19 | 337 |
| Status | Accuracy | Program |
|---|---|---|
| 62.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) | |
| ▶ | 62.2% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
| 62.2% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| 62.3% | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| ▶ | 36.5% | (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
| 62.3% | (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) | |
| 35.8% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 36.3% | (-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| ▶ | 61.8% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 62.1% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ▶ | 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
| 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) | |
| 32.3% | (-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) | |
| 36.7% | (-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.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 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
| 99.4% | #s(approx (- (tan (+ x eps)) (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)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
Compiled 897 to 444 computations (50.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 26496 | (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) | |
| cost-diff | 320 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| cost-diff | 1408 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 0 | #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) | |
| cost-diff | 192 | (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) | |
| cost-diff | 5824 | (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) | |
| cost-diff | 26816 | (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
| 15 148× | lower-fma.f32 |
| 15 134× | lower-fma.f64 |
| 3 522× | lower-*.f32 |
| 3 518× | lower-*.f64 |
| 2 722× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 715 |
| 0 | 104 | 707 |
| 1 | 185 | 625 |
| 2 | 417 | 622 |
| 3 | 1101 | 622 |
| 4 | 3896 | 612 |
| 5 | 6856 | 612 |
| 0 | 8076 | 602 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
eps |
(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) |
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) |
(+.f64 (pow.f64 (sin.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 2 binary64)) |
(sin.f64 x) |
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) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 1/6 binary64) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64) |
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.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) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 x x) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(literal 2 binary64) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 1/3 binary64))) (*.f64 eps (*.f64 eps eps)) (fma.f64 (/.f64 eps (cos.f64 x)) (fma.f64 eps (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(fma.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 1/3 binary64))) (*.f64 eps (*.f64 eps eps)) (fma.f64 (/.f64 eps (cos.f64 x)) (fma.f64 eps (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)) |
eps |
(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 1/3 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(fma.f64 eps (+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 1/3 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) |
(+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 1/3 binary64))) |
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
(+.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 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 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) |
(+.f64 (pow.f64 (sin.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 2 binary64)) |
(sin.f64 x) |
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) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 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)) |
#s(literal 1/6 binary64) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal -1/6 binary64) |
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.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) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 x x) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(tan.f64 x) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(*.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 1 binary64)) |
(-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(literal 2 binary64) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.26171875 | (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) | |
| accuracy | 0.2890625 | (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | |
| accuracy | 11.74860600147185 | (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 28.677149210731432 | (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) | |
| accuracy | 0.00390625 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 0.0078125 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) | |
| accuracy | 0.03125 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 24.180021715379446 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.01171875 | (/.f64 #s(literal 1 binary64) (tan.f64 x)) | |
| accuracy | 0.0234375 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.1484375 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| accuracy | 24.126973597640735 | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| accuracy | 0.0234375 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.390625 | (*.f64 x #s(literal 1/3 binary64)) | |
| accuracy | 0.441805837819607 | #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) | |
| accuracy | 24.126973597640735 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) | |
| accuracy | 0.03972626953688403 | (pow.f64 (sin.f64 x) #s(literal 3 binary64)) | |
| accuracy | 0.052108789073768064 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.15234375 | (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| accuracy | 0.990566259768442 | (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) |
| 86.0ms | 91× | 1 | valid |
| 70.0ms | 159× | 0 | valid |
| 13.0ms | 4× | 3 | valid |
| 2.0ms | 2× | 2 | valid |
Compiled 643 to 59 computations (90.8% saved)
ival-div: 23.0ms (16.9% of total)ival-add: 19.0ms (14% of total)ival-mult: 16.0ms (11.8% of total)adjust: 13.0ms (9.6% of total)ival-pow2: 12.0ms (8.8% of total)const: 10.0ms (7.4% of total)ival-pow: 10.0ms (7.4% of total)ival-sin: 10.0ms (7.4% of total)ival-tan: 8.0ms (5.9% of total)ival-sub: 6.0ms (4.4% of total)ival-cos: 5.0ms (3.7% of total)ival-neg: 1.0ms (0.7% 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 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (patch (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) #<representation binary64>) () ()) |
#s(alt (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (patch (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) #<representation binary64>) () ()) |
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) (patch (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) 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 #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) (patch #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ()) |
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (patch (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ()) |
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (patch (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #<representation binary64>) () ()) |
#s(alt (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.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 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 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 (*.f64 x #s(literal 1/3 binary64)) (patch (*.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* -1/3 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.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 (+ (* x (- 2 (* -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 (- (+ 2 (/ (* 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 (- (+ 2 (* x (- (* 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 (+.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)) (/ (sin (+ eps x)) (cos (+ eps 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 x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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 x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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 x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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 x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 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 x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 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 x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 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 x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 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 (* 2 (/ (sin x) (cos x))) (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 (+ (* 2 (/ (sin x) (cos x))) (* 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 (+ (* 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)))))) (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 (+ (* 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)))))) (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)) (/ (sin (+ eps x)) (cos (+ eps 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) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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) (cos x)) (/ (sin (+ eps x)) (cos (+ eps 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) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) (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) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) (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) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) (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) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) (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>) () ())) ()) |
114 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 11.0ms | x | @ | -inf | (* x 1/3) |
| 7.0ms | x | @ | inf | (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 4.0ms | x | @ | -inf | (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 3.0ms | eps | @ | 0 | (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) |
| 3.0ms | x | @ | inf | (/ 1 (cos (+ x eps))) |
| 1× | egg-herbie |
| 9 912× | lower-fma.f64 |
| 9 912× | lower-fma.f32 |
| 6 442× | lower-*.f64 |
| 6 442× | lower-*.f32 |
| 4 356× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 679 | 12664 |
| 1 | 2100 | 12157 |
| 2 | 7033 | 12063 |
| 0 | 8080 | 11661 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-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) |
(- (+ (* -1/2 (/ (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) |
(- (+ (* -1/2 (/ (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) |
(* 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 (+ (/ (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 eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 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 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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))))) |
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))))))) |
(- (+ 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))))) |
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(- (+ 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))))) |
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(/ (sin eps) (cos eps)) |
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -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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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
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(/ (sin eps) (cos eps)) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin x) (cos x)) |
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(/ (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 (* -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 |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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 x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos 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 x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin eps) (cos eps)) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
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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 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 (* -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 (- 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 (+ 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 (- 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 eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
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(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
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(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 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)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 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)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (+ (* x (- (+ (* -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))) (/ (* (cos eps) (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (sin eps))))) (+ 1/6 (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (sin eps)))))) (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps))) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (* eps (- (* 1/2 (/ (* (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)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -2 (/ (* (sin x) (+ (* -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))))) (cos x))) (/ (* (pow (sin x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/2 (/ (* (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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* 1/2 (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (sin x)))))))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (pow (sin eps) 2) (pow (cos eps) 2)) |
(+ (* 2 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (+ (* 2 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* x (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (+ (* 2 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* x (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* x (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2))) 1)))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* 2 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) |
(* eps (+ (* 2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* eps (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))))) |
(* eps (+ (* 2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* eps (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* eps (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) |
(* eps (+ (* 2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* eps (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* eps (+ (* -2 (/ (* (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))) (+ (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))) (* eps (+ (* -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)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -2 (/ (* (sin x) (+ (* -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))))) (cos x))) (/ (* (pow (sin x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (cos x) 2)))))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin eps) 2) (pow (cos eps) 2)) |
(+ (* 2 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (+ (* 2 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* x (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (+ (* 2 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* x (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* x (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) |
(/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) |
(/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) |
(/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* 2 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* 2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* eps (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* 2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* eps (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* eps (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) |
(/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) |
(/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) |
(/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) |
(/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 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 (+ (/ (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 eps 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 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 (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(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)))) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(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)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 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)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 2 (/ (* 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 (- (+ 2 (* x (- (* 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 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 (* -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))))) |
(* 2 (/ (sin x) (cos x))) |
(+ (* 2 (/ (sin x) (cos x))) (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* 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)))))) |
(+ (* 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 (+ 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 (- 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))))) |
| Outputs |
|---|
-1/2 |
#s(literal -1/2 binary64) |
(- (* -1/3 (pow x 2)) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/9 binary64) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -17/135 binary64) #s(literal -2/9 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) |
(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 -1/2 binary64)) |
(* eps (+ 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) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 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)))))) |
(*.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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 eps (*.f64 eps eps))) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (*.f64 eps (*.f64 eps 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) (+.f64 (+.f64 #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))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps 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) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (+.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 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (+.f64 (/.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)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps 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) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (+.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 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (+.f64 (/.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)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))) |
(* (pow eps 3) (- (+ 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)))))) |
(*.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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 eps (*.f64 eps eps))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (-.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (-.f64 (/.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 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps)))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (/.f64 (-.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 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) 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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (/.f64 (-.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 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) 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) (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))) |
(+ eps (* 1/3 (pow eps 3))) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(fma.f64 x (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (* 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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1/3 |
#s(literal 1/3 binary64) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* x (+ 1 (/ eps x))) |
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(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
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(* -1 (* x (- (* -1 (/ eps x)) 1))) |
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eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
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(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* 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))))) |
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(- (/ (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))) |
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(- (/ (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))) |
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
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(/ (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
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(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
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(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
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(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
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(fma.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (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))))) (/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (cos.f64 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)))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (sin.f64 x)) (cos.f64 x))) |
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
(+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) |
| 5 598× | lower-fma.f32 |
| 5 584× | lower-fma.f64 |
| 4 652× | lower-*.f32 |
| 4 648× | lower-*.f64 |
| 2 368× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 438 |
| 0 | 104 | 411 |
| 1 | 471 | 305 |
| 2 | 4248 | 297 |
| 0 | 8129 | 287 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) |
(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.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 4 binary64)) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(*.f64 x #s(literal 1/3 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) |
(+.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) |
(+.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))))) |
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 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 -1/2 binary64)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) |
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(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal -1 binary64) (tan.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))) |
(/.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) |
(/.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal -1 binary64) (tan.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))) |
(/.f64 (fma.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 (fma.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 (+.f64 x eps)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 (+.f64 x eps)))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(/.f64 (+.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (sin.f64 (+.f64 x eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (cos.f64 (+.f64 x eps)))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(/.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(pow.f64 (/.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(*.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (neg.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) |
Compiled 55 899 to 3 265 computations (94.2% saved)
21 alts after pruning (18 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 469 | 13 | 1 482 |
| Fresh | 8 | 5 | 13 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 480 | 21 | 1 501 |
| Status | Accuracy | Program |
|---|---|---|
| 62.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) | |
| ✓ | 62.2% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
| 62.2% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| ▶ | 36.5% | (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
| 62.3% | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| ✓ | 36.5% | (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
| 62.3% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) | |
| 35.8% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 36.3% | (-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) | |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ▶ | 99.4% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) | |
| ▶ | 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
| ▶ | 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
Compiled 994 to 489 computations (50.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) | |
| cost-diff | 0 | (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) | |
| cost-diff | 320 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| cost-diff | 0 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) | |
| cost-diff | 0 | #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) | |
| cost-diff | 704 | (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) | |
| cost-diff | 0 | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) | |
| cost-diff | 0 | #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) | |
| cost-diff | 0 | (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) | |
| cost-diff | 128 | (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) | |
| cost-diff | 128 | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) | |
| cost-diff | 6272 | (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) | |
| cost-diff | 13056 | (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
| 15 946× | lower-fma.f32 |
| 15 920× | lower-fma.f64 |
| 4 256× | lower-*.f32 |
| 4 238× | lower-*.f64 |
| 3 514× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 99 | 1160 |
| 0 | 168 | 1160 |
| 1 | 325 | 1086 |
| 2 | 746 | 1082 |
| 3 | 2145 | 1058 |
| 4 | 6583 | 1048 |
| 0 | 8118 | 1000 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
#s(literal 1/2 binary64) |
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.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)) |
#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)) |
(cos.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
eps |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
(fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
x |
(fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
(*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 4/3 binary64) |
(*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) |
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps 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 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
eps |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 x eps)) |
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) |
(-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) |
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(fma.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)) |
#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)) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(cos.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
eps |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) (*.f64 x (+.f64 x eps)) (*.f64 eps (+.f64 x eps))) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) (*.f64 x (+.f64 x eps)) (*.f64 eps (+.f64 x eps))) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps))) |
(fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) (*.f64 x (+.f64 x eps)) (*.f64 eps (+.f64 x eps))) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)) |
x |
(fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) (*.f64 x (+.f64 x eps)) (*.f64 eps (+.f64 x eps))) |
(*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(*.f64 x (*.f64 eps (*.f64 eps #s(literal 4/3 binary64)))) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) |
(*.f64 eps eps) |
eps |
#s(literal 4/3 binary64) |
(*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) |
(*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)) |
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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 (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (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)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (/.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 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) |
eps |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 x eps)) |
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.2578125 | (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) | |
| accuracy | 0.2890625 | (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | |
| accuracy | 11.762638992565432 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) | |
| accuracy | 28.677149210731432 | (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) | |
| accuracy | 0.01171875 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.01171875 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.03125 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.37688180858561326 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) | |
| accuracy | 0.140625 | (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.203125 | (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal 1/3 binary64)) | |
| accuracy | 0.5113135272856223 | #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) | |
| accuracy | 0 | (*.f64 eps eps) | |
| accuracy | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) | |
| accuracy | 0.1953125 | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) | |
| accuracy | 29.97187098748631 | #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) | |
| accuracy | 0.03515625 | (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) | |
| accuracy | 0.13671875 | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) | |
| accuracy | 0.15234375 | (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 29.93284566980984 | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| 427.0ms | 237× | 1 | valid |
| 19.0ms | 4× | 3 | valid |
| 12.0ms | 13× | 0 | valid |
| 7.0ms | 2× | 2 | valid |
Compiled 883 to 95 computations (89.2% saved)
ival-cos: 69.0ms (17.8% of total)ival-mult: 63.0ms (16.3% of total)ival-add: 54.0ms (13.9% of total)adjust: 53.0ms (13.7% of total)ival-div: 33.0ms (8.5% of total)ival-pow: 28.0ms (7.2% of total)const: 26.0ms (6.7% of total)ival-pow2: 22.0ms (5.7% of total)ival-tan: 15.0ms (3.9% of total)ival-sub: 13.0ms (3.4% of total)ival-sin: 10.0ms (2.6% of total)ival-neg: 2.0ms (0.5% of total)exact: 1.0ms (0.3% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (patch (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) #<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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (patch (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) #<representation binary64>) () ()) |
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#s(alt #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (patch #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (patch (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) (patch #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) (patch (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) (patch #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ()) |
#s(alt (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (patch (/.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 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (patch (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ()) |
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (patch (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 eps eps) (patch (*.f64 eps eps) #<representation binary64>) () ()) |
#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (patch (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (patch (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#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 (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (patch (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (patch (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) #<representation binary64>) () ())) ()) |
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#s(alt (+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) (taylor 0 eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* eps (+ (* -1 (* (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)))))))) (+ (* -1/2 (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1/6 (sin x)) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) (taylor 0 eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (patch (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
144 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | x | @ | 0 | (+ (* (/ 1 (cos (+ x eps))) (* (sin (+ x eps)) (tan (+ x eps)))) (neg (pow (tan x) 2))) |
| 5.0ms | x | @ | -inf | (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) |
| 4.0ms | x | @ | inf | (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) |
| 3.0ms | eps | @ | 0 | (+ (* (/ 1 (cos (+ x eps))) (* (sin (+ x eps)) (tan (+ x eps)))) (neg (pow (tan x) 2))) |
| 3.0ms | eps | @ | 0 | (/ (+ (* (/ 1 (cos (+ x eps))) (* (sin (+ x eps)) (tan (+ x eps)))) (neg (pow (tan x) 2))) (+ (tan (+ x eps)) (tan x))) |
| 1× | egg-herbie |
| 7 686× | lower-fma.f64 |
| 7 686× | lower-fma.f32 |
| 6 878× | lower-+.f64 |
| 6 878× | lower-+.f32 |
| 6 408× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1088 | 22971 |
| 1 | 3518 | 22200 |
| 0 | 8478 | 21328 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* 1/3 eps) |
(+ x (* 1/3 eps)) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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 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 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))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(/ (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 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 (* -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 (- 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 (+ 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 (- 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))) |
(* 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 (+ (/ (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 eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 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 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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))))) |
(/ (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 (+ (/ (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 eps 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* (pow eps 2) (- (+ 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)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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 (+ (/ (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)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(pow eps 2) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* eps x) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* 4/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* 4/3 (* (pow eps 3) x)) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) 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 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 (* -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 (- 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 (+ 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 (- 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))) |
(* 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 (+ (/ (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 eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 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 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 3) (pow x 3))) (+ (* 4/3 (pow eps 2)) (+ (/ eps (pow x 3)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))) x))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (+ (* x (- (+ (* -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))) (/ (* (cos eps) (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (sin eps))))) (+ 1/6 (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (sin eps)))))) (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps))) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (* eps (- (* 1/2 (/ (* (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)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -2 (/ (* (sin x) (+ (* -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))))) (cos x))) (/ (* (pow (sin x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/2 (/ (* (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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* 1/2 (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (sin x)))))))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(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)))))))) |
(/ (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)) |
(/ (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 x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(/ (pow (sin eps) 2) (pow (cos eps) 2)) |
(+ (* x (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (- (+ (* x (- (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2)) (+ (* -1 (/ (* (sin eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(+ (* x (- (+ (* x (- (+ (* x (- (+ (* -1 (/ (* (sin eps) (+ 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))))))) (cos eps))) (+ (* -1/2 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (+ (* -1/6 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (+ 1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (+ (* -1/2 (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* 1/6 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* eps (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (- (+ (* eps (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (- (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1 (/ (* (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))) (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/6 (/ (sin x) (cos x))) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (* 1/6 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2)))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (- (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1 (/ (* (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))) (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/6 (/ (sin x) (cos x))) (+ (* eps (- (+ (* -1 (+ 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) (+ (* -1/2 (/ (* (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))))) (cos x))) (+ (* -1/2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/6 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (+ (* -1 (/ (* (sin x) (- (+ (* -1 (/ (* (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))) (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/6 (/ (sin x) (cos x))) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (* 1/6 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* 1/6 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))))))) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (* 1/6 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2)))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (cos eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (sin eps))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* x (- (/ (* (cos eps) (- (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2)) (+ (* -1 (/ (* (sin eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (cos eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (sin eps))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (/ (* (cos eps) (- (+ (/ (sin eps) (cos eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (sin eps)))) 2)) (/ (sin eps) (cos eps))) |
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(/ (pow (sin x) 3) (pow (cos x) 3)))))) (pow (sin x) 2)))))) (sin x))))))) (* 1/4 (/ (* (pow (cos x) 2) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3)))))) (pow (sin x) 2))))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 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))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 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))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 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)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 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)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 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))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* eps x) |
(* eps (+ eps x)) |
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x)))))) |
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x)))))) |
(* 4/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 4/3 x) (/ 1 eps))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* 4/3 (* (pow eps 3) x)) |
(* -1 (* (pow eps 3) (- (* -4/3 x) (/ 1 eps)))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))))) |
(pow eps 2) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(* eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x))) |
(* eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 2 (/ (* 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 (- (+ 2 (* x (- (* 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 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 (* -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))))) |
(* 2 (/ (sin x) (cos x))) |
(+ (* 2 (/ (sin x) (cos x))) (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* 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)))))) |
(+ (* 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 (+ 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 (- 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))))) |
(/ (pow (sin eps) 2) (cos eps)) |
(+ (* x (+ (sin eps) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (cos eps))) |
(+ (* x (+ (sin eps) (+ (* x (+ (* -1/2 (/ (pow (sin eps) 2) (cos eps))) (+ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (/ (pow (sin eps) 2) (cos eps))) |
(+ (* x (+ (sin eps) (+ (* x (+ (* -1/2 (/ (pow (sin eps) 2) (cos eps))) (+ (* x (+ (* -1 (* (sin eps) (+ 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)))))))) (+ (* -1/2 (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ (* -1/6 (sin eps)) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))))) (+ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (/ (pow (sin eps) 2) (cos eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/ (pow (sin x) 2) (cos x)) |
(+ (* eps (+ (sin x) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (cos x))) |
(+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) |
(+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* eps (+ (* -1 (* (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)))))))) (+ (* -1/2 (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1/6 (sin x)) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
| Outputs |
|---|
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 eps (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 eps (-.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 eps (-.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 eps (-.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 eps (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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)))))) (neg.f64 eps)) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ x (* 1/3 eps)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
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(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
(fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
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(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (pow x 2))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(/ (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))) |
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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))) |
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(- (/ (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 (* -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))) |
(* 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))))) |
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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))))) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 eps (neg.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (*.f64 (sin.f64 x) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* 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))))) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 eps (neg.f64 (fma.f64 eps (fma.f64 (/.f64 (*.f64 (sin.f64 x) (+.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)) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (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 1/6 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (/.f64 (*.f64 (sin.f64 x) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (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 (- 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))) |
(* 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))))) |
(fma.f64 eps (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 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 (+ (* 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 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 eps (*.f64 eps eps))) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (+.f64 (/.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 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (/.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))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)))) (+.f64 (+.f64 (/.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 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (/.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)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps))))) (/.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 eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
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(* 4/3 (* (pow eps 2) (pow x 2))) |
(*.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)) (*.f64 x x)) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(*.f64 (*.f64 x x) (fma.f64 eps (/.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (/.f64 (*.f64 eps eps) x)) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (/.f64 (*.f64 eps eps) x)) x))) |
(* eps x) |
(*.f64 x eps) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x (+.f64 x eps)) #s(literal 1 binary64)) x)) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x (+.f64 x eps)) #s(literal 1 binary64)) x)) |
(* 4/3 (* (pow eps 3) x)) |
(*.f64 #s(literal 4/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal 4/3 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) eps))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal 4/3 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 x (*.f64 eps eps))))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal 4/3 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 x (*.f64 eps eps))))) |
(* 4/3 (* (pow eps 3) x)) |
(*.f64 #s(literal 4/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
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(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
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(/ (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))) |
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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))) |
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(- (/ (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 (* -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))) |
(* 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))))) |
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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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(- (/ (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 (- 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))) |
(* 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))))) |
(fma.f64 eps (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 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 (+ (* 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 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.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 eps (*.f64 eps eps))) |
(* (pow eps 3) (- (+ 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)))))) |
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eps |
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(pow x 2) |
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(pow x 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
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(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(* eps (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (- (+ (* eps (- (+ 1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1 (/ (* (sin x) (- (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
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(fma.f64 x (fma.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)))) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (fma.f64 (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)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.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)) (cos.f64 eps))) |
(+ (* x (+ (sin eps) (+ (* x (+ (* -1/2 (/ (pow (sin eps) 2) (cos eps))) (+ (* x (+ (* -1 (* (sin eps) (+ 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)))))))) (+ (* -1/2 (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (+ (* -1/6 (sin eps)) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))))) (+ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (/ (pow (sin eps) 2) (cos eps))) |
(fma.f64 x (fma.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)))) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (fma.f64 x (fma.f64 (+.f64 #s(literal 1/6 binary64) (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))) (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)))))) (neg.f64 (sin.f64 eps)) (fma.f64 (sin.f64 eps) (+.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 -1/6 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.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))))))) (fma.f64 (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)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.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)) (cos.f64 eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- eps (* -1 x))) 2) (cos (- eps (* -1 x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin x) 2) (cos x)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) |
(+ (* eps (+ (sin x) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (cos x))) |
(fma.f64 eps (*.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)))) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) |
(+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) |
(fma.f64 eps (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)))) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (fma.f64 (cos.f64 x) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) |
(+ (* eps (+ (sin x) (+ (* eps (+ (* -1/2 (/ (pow (sin x) 2) (cos x))) (+ (* eps (+ (* -1 (* (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)))))))) (+ (* -1/2 (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1/6 (sin x)) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (+ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (pow (sin x) 2) (cos x))) |
(fma.f64 eps (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)))) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (fma.f64 eps (-.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)))) #s(literal -1/6 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (+.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 (sin.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (fma.f64 (cos.f64 x) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (+ eps x)) 2) (cos (+ eps x))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
(/ (pow (sin (- x (* -1 eps))) 2) (cos (- x (* -1 eps)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (cos.f64 (+.f64 x eps))) |
| 4 926× | lower-fma.f32 |
| 4 902× | lower-fma.f64 |
| 3 640× | lower-*.f32 |
| 3 622× | lower-*.f64 |
| 2 574× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 97 | 874 |
| 0 | 164 | 872 |
| 1 | 756 | 620 |
| 2 | 7370 | 620 |
| 0 | 8268 | 615 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (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)) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
(fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps 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 2 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(*.f64 eps eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(*.f64 (sin.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) |
| Outputs |
|---|
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(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
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(fma.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (*.f64 eps eps)) |
(/.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64))) (fma.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (-.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (*.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 eps eps))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (-.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 eps eps))) |
(/.f64 (*.f64 eps (fma.f64 eps (*.f64 eps eps) (*.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)))))) (fma.f64 eps (-.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x))))) |
(/.f64 (*.f64 eps (*.f64 (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (-.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps))) (-.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps)) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x))))) eps) (fma.f64 eps (-.f64 eps (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (-.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps)) eps) (-.f64 (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) x) eps)) |
(*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) eps) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 (+.f64 x x)))))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) (neg.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))) |
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 2 binary64)) |
(*.f64 (cos.f64 x) (cos.f64 x)) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (exp.f64 (log.f64 (cos.f64 x))) (exp.f64 (log.f64 (cos.f64 x)))) |
(*.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) |
(+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 (+.f64 eps x))) |
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (tan.f64 x)) |
(fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(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)))) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64)))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (sin.f64 x) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/.f64 (fma.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) |
(/.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(*.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(+.f64 (*.f64 (tan.f64 (+.f64 eps x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (tan.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (tan.f64 (+.f64 eps x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (tan.f64 (+.f64 eps x)) (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (tan.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(fma.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (tan.f64 (+.f64 eps x)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (tan.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (cos.f64 (+.f64 eps x))) |
(/.f64 (*.f64 (sin.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
(/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
(*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (+.f64 eps x)) (tan.f64 (+.f64 eps x)))) |
(*.f64 (sin.f64 (+.f64 eps x)) (tan.f64 (+.f64 eps x))) |
(*.f64 (tan.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(*.f64 (*.f64 (sin.f64 (+.f64 eps x)) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) (tan.f64 (+.f64 eps x))) |
Compiled 63 220 to 3 614 computations (94.3% saved)
16 alts after pruning (15 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 223 | 13 | 1 236 |
| Fresh | 11 | 2 | 13 |
| Picked | 5 | 0 | 5 |
| Done | 2 | 1 | 3 |
| Total | 1 241 | 16 | 1 257 |
| Status | Accuracy | Program |
|---|---|---|
| 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) | |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
| 99.4% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.3% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| ▶ | 99.3% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
| 99.2% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) | |
| ▶ | 99.0% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) | |
| ▶ | 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) | |
| 36.3% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
Compiled 677 to 344 computations (49.2% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| cost-diff | 0 | #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) | |
| cost-diff | 0 | (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) | |
| cost-diff | 0 | #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) | |
| cost-diff | 0 | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| cost-diff | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| cost-diff | 0 | (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| cost-diff | 6272 | (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
| 15 688× | lower-fma.f32 |
| 15 660× | lower-fma.f64 |
| 5 128× | lower-*.f32 |
| 5 114× | lower-*.f64 |
| 3 674× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 112 | 990 |
| 0 | 159 | 974 |
| 1 | 354 | 946 |
| 2 | 865 | 922 |
| 3 | 2528 | 914 |
| 4 | 6503 | 894 |
| 0 | 8145 | 859 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) |
#s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) |
#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)) |
(sin.f64 x) |
x |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(cos.f64 x) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x x) |
x |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
(fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
x |
#s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
eps |
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
#s(literal 4/3 binary64) |
(*.f64 x x) |
#s(literal 1 binary64) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(*.f64 eps eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x #s(literal 2/15 binary64)) |
#s(literal 2/15 binary64) |
#s(literal 1/3 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) |
#s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) |
#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)) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #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) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x)) |
(*.f64 x x) |
x |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
(fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)) eps))) |
(fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)) eps)) |
x |
#s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) |
#s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 eps (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)) |
eps |
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) |
#s(literal 4/3 binary64) |
(*.f64 x x) |
#s(literal 1 binary64) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)) eps) |
(*.f64 eps eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) |
(*.f64 x #s(literal 2/15 binary64)) |
#s(literal 2/15 binary64) |
#s(literal 1/3 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0625 | (*.f64 x (*.f64 x x)) | |
| accuracy | 0.07421875 | (*.f64 x #s(literal 2/15 binary64)) | |
| accuracy | 0.18252839838699658 | #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| accuracy | 24.126973597640735 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| accuracy | 0.058981185195622204 | #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) | |
| accuracy | 0.140625 | (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal 1/3 binary64)) | |
| accuracy | 0.5113135272856223 | #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) | |
| accuracy | 0.01953125 | (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) | |
| accuracy | 0.01953125 | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) | |
| accuracy | 0.19267404658983583 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 0.37688180858561326 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| accuracy | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 0.37688180858561326 | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| accuracy | 1.2692772341844423 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| accuracy | 0.015625 | (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) | |
| accuracy | 0.01953125 | (pow.f64 (tan.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.15234375 | (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 1.3761414803446825 | #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) |
| 329.0ms | 89× | 1 | valid |
| 120.0ms | 162× | 0 | valid |
| 15.0ms | 3× | 3 | valid |
| 4.0ms | 2× | 2 | valid |
Compiled 641 to 109 computations (83% saved)
ival-mult: 207.0ms (49.2% of total)ival-add: 67.0ms (15.9% of total)ival-div: 29.0ms (6.9% of total)const: 27.0ms (6.4% of total)adjust: 24.0ms (5.7% of total)ival-cos: 19.0ms (4.5% of total)ival-pow2: 15.0ms (3.6% of total)ival-pow: 10.0ms (2.4% of total)ival-sub: 9.0ms (2.1% of total)ival-tan: 8.0ms (1.9% of total)ival-sin: 4.0ms (1% of total)exact: 1.0ms (0.2% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#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 #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) (patch #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) (patch #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) (patch #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) #<representation binary64>) () ()) |
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#s(alt (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) (patch (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) (patch #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) (patch (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) #<representation binary64>) () ()) |
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#s(alt (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) (patch (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) 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 #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) (patch #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (patch #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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>) () ()) |
#s(alt (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (patch (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) #<representation binary64>) () ()) |
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#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt x (taylor 0 x) (#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 (* x (+ 1 (* 5/6 (pow x 2)))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) (taylor 0 x) (#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 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) (taylor 0 x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor inf x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor inf x) (#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>) () ())) ()) |
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#s(alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor inf x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor -inf x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor -inf x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor -inf x) (#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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (taylor -inf x) (#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>) () ())) ()) |
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#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor 0 eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor 0 eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor 0 eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor 0 eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor -inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor -inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor -inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 eps) (taylor -inf eps) (#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* eps x) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) (taylor -inf eps) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps x) (pow eps 2)) (taylor 0 x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) (taylor 0 x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) (taylor 0 x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 4/3 (* (pow eps 2) (pow x 2))) (taylor inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) (taylor inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 4/3 (* (pow eps 2) (pow x 2))) (taylor -inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) (taylor -inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) (taylor -inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) (taylor -inf x) (#s(alt (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) (patch (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 2/15 x) (taylor -inf x) (#s(alt (*.f64 x #s(literal 2/15 binary64)) (patch (*.f64 x #s(literal 2/15 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor 0 x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (pow x 3) (taylor -inf x) (#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ())) ()) |
132 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | x | @ | 0 | (* (* x x) (+ (* (* x x) (+ (* (* x x) 17/45) 2/3)) 1)) |
| 1.0ms | eps | @ | inf | (+ (* (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) eps) eps) |
| 1.0ms | x | @ | -inf | (+ (* (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) eps) eps) |
| 1.0ms | x | @ | inf | (+ (* (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) eps) eps) |
| 1.0ms | eps | @ | -inf | (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) |
| 1× | egg-herbie |
| 9 728× | lower-fma.f64 |
| 9 728× | lower-fma.f32 |
| 6 858× | lower-*.f64 |
| 6 858× | lower-*.f32 |
| 5 226× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 733 | 17606 |
| 1 | 2396 | 16946 |
| 0 | 8153 | 16148 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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 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 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) (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 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 (* -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 (- 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 (+ 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 (- 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))) |
(* 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (+ (* x (- (+ (* -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))) (/ (* (cos eps) (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (sin eps))))) (+ 1/6 (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (sin eps)))))) (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps))) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (* eps (- (* 1/2 (/ (* (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)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -2 (/ (* (sin x) (+ (* -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))))) (cos x))) (/ (* (pow (sin x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/2 (/ (* (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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* 1/2 (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (sin x)))))))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(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)))))))) |
(/ (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)) |
(/ (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 x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(/ (sin eps) (cos eps)) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* x (- (+ (* x (- (+ (* -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))) (/ (* (cos eps) (+ (* -2 (/ (* (sin eps) (+ 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))))))) (cos eps))) (* 2 (/ (* (sin eps) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (cos eps))))) (sin eps))))) (+ 1/6 (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2)) (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps)) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (sin eps)))))) (/ (* (cos eps) (- (+ (* 2 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) 1)) (sin eps))) (+ (/ (* (cos eps) (* (- 2 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* 2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) 2))) (sin eps)) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))))) 2)) (/ (sin eps) (cos eps))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* eps (- (+ (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (* eps (- (* 1/2 (/ (* (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)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -2 (/ (* (sin x) (+ (* -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))))) (cos x))) (/ (* (pow (sin x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/2 (/ (* (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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* 1/2 (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* -2 (/ (* (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))) (* 2 (/ (* (sin x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (cos x))))) (sin x))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (sin x)))))))) (+ (* 1/2 (/ (* (cos x) (* (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (- (* 1/2 (/ (* (cos x) (+ (* 2 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (sin x))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (sin x))) (* 1/2 (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)))))) (* 1/2 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(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)))))))) |
(/ (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)) |
(/ (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 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 (* 17/45 (pow x 2)))))) |
(* 17/45 (pow x 6)) |
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(* 17/45 (pow x 6)) |
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
(/ (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 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 (* -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 (- 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 (+ 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 (- 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))) |
(* 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 (+ (/ (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 eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(* (pow eps 3) (- (+ 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 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(* -1 (* (pow eps 3) (+ (* -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 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 3) (pow x 3))) (+ (* 4/3 (pow eps 2)) (+ (/ eps (pow x 3)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))) x))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(pow eps 2) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* eps x) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* 4/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* 4/3 (* (pow eps 3) x)) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) 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 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 (* -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 (- 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 (+ 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 (- 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)) |
(+ (* 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 x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps 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)) |
(+ (* 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 (+ 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 (* -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 |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
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 x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos 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))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 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)))))))) |
(/ (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)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* 1/3 eps) |
(+ x (* 1/3 eps)) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
2/3 |
(+ 2/3 (* 17/45 (pow x 2))) |
(+ 2/3 (* 17/45 (pow x 2))) |
(+ 2/3 (* 17/45 (pow x 2))) |
(* 17/45 (pow x 2)) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* 17/45 (pow x 2)) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* 1/3 eps) |
(* eps x) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(pow eps 2) |
(+ (* eps x) (pow eps 2)) |
(+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) |
(+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(* 2/15 x) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
| Outputs |
|---|
x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (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 x (fma.f64 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)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.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 (- (* -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 x (fma.f64 x (fma.f64 (+.f64 #s(literal 1/2 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 (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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (neg.f64 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)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (/.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))) |
(- (/ (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 (* -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))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (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))))) |
(+.f64 eps (*.f64 eps (fma.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)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* 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))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (+.f64 #s(literal 1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (neg.f64 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))) (+.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 (- (+ 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))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (fma.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)))) (cos.f64 x)) #s(literal -1/3 binary64) (*.f64 (+.f64 #s(literal 1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 eps) #s(literal -1/6 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.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))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (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 (- 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))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (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))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (*.f64 eps (*.f64 eps eps))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (*.f64 eps (*.f64 eps eps))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 eps)) (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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)))))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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))))) |
(*.f64 (-.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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)))))) (/.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.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)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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))))) |
(*.f64 (-.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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)))))) (/.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.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)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(+ eps (* 1/3 (pow eps 3))) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(fma.f64 x (*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) eps)) (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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)) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* 1/3 (pow eps 2)) |
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eps |
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(/ (- (/ (pow (sin (- eps (* -1 x))) 2) (pow (cos (- eps (* -1 x))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))) |
(/ (- (/ (pow (sin (+ eps x)) 2) (pow (cos (+ eps x)) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (+ eps x)) (cos (+ eps x))))) |
(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))) |
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(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))) |
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(/ (- (/ (pow (sin (- x (* -1 eps))) 2) (pow (cos (- x (* -1 eps))) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (cos x)) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))) |
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eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps)) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
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(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 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 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
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(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
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(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
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(/ (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))) |
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
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(* 17/45 (pow x 6)) |
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(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
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(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
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(* 17/45 (pow x 6)) |
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(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
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(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
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(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) |
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(/ (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (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))))) |
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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))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (fma.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)))) (cos.f64 x)) #s(literal -1/3 binary64) (*.f64 (+.f64 #s(literal 1/6 binary64) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 eps) #s(literal -1/6 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.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))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (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 (- 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))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (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))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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))))) |
(* (pow eps 3) (- (+ 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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (+.f64 (/.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 3 binary64)) (*.f64 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 (*.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 eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) (+.f64 (/.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 3 binary64)) (*.f64 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 (*.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 eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) (+.f64 (/.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 3 binary64)) (*.f64 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 (*.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 eps 3) (- (+ 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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.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 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 eps (*.f64 (*.f64 eps eps) (neg.f64 (+.f64 (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps))))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (neg.f64 (+.f64 (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.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)))))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (neg.f64 (+.f64 (+.f64 #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))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.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 (* 1/3 (pow eps 3))) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(fma.f64 x (*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps)) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) eps)) (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
(+ eps (* eps (+ (* 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 x) |
(+.f64 x eps) |
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x |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
x |
(+ eps x) |
(+.f64 x eps) |
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(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal 1/3 binary64))) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) |
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(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ x (* 1/3 eps)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(+.f64 x (*.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
2/3 |
#s(literal 2/3 binary64) |
(+ 2/3 (* 17/45 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
(+ 2/3 (* 17/45 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
(+ 2/3 (* 17/45 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
(* 17/45 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 17/45 binary64)) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* 17/45 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 17/45 binary64)) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 x x))) x) x) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(* eps x) |
(*.f64 x eps) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) x)) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) x)) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) x)) |
(* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1 (* 4/3 (pow x 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (/.f64 x eps)))) |
(pow eps 2) |
(*.f64 eps eps) |
(+ (* eps x) (pow eps 2)) |
(*.f64 eps (+.f64 x eps)) |
(+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) |
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) x)) |
(+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2)) |
(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1 binary64)) x)) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(*.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (fma.f64 eps (/.f64 eps (*.f64 x x)) (/.f64 eps x)))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (fma.f64 eps (/.f64 eps (*.f64 x x)) (/.f64 eps x)))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(*.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ eps x))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 (neg.f64 (fma.f64 eps (/.f64 eps x) eps)) (neg.f64 x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 (neg.f64 (fma.f64 eps (/.f64 eps x) eps)) (neg.f64 x)))) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(* 2/15 x) |
(*.f64 x #s(literal 2/15 binary64)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
| 6 204× | lower-fma.f32 |
| 6 176× | lower-fma.f64 |
| 4 560× | lower-*.f32 |
| 4 546× | lower-*.f64 |
| 3 088× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 112 | 887 |
| 0 | 159 | 854 |
| 1 | 863 | 718 |
| 0 | 8356 | 690 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(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 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps))) |
(fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)) |
#s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
#s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #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 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) |
(*.f64 eps #s(literal 1/3 binary64)) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 x #s(literal 2/15 binary64)) |
(*.f64 x (*.f64 x x)) |
| Outputs |
|---|
(+.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) |
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)) |
(-.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (/.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))))) |
(-.f64 (/.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x) (sin.f64 x)) |
(fma.f64 (tan.f64 x) (*.f64 (tan.f64 x) (sin.f64 x)) (sin.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(fma.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (tan.f64 x) (sin.f64 x)) |
(fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (sin.f64 x)) |
(fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x)) |
(fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (sin.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (sin.f64 x)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (sin.f64 x)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (sin.f64 x)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (cos.f64 x)) (sin.f64 x)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))) (-.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)) (-.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) |
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64)))))) |
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64)))) |
(/.f64 (-.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) |
(/.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (-.f64 (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)))) |
(*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))))))) |
(*.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))))) |
(*.f64 (-.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))))) |
(*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x)))) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(+.f64 (*.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 eps))) (/.f64 (*.f64 eps eps) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 eps)))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
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(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 x #s(literal 17/45 binary64)) x #s(literal 2/3 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) #s(literal 8/27 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal -2/3 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) #s(literal -4/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) #s(literal 8/27 binary64)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) #s(literal 8/27 binary64)) (+.f64 #s(literal 4/9 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) (*.f64 (*.f64 x x) #s(literal 34/135 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) #s(literal -4/9 binary64)) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal -2/3 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) #s(literal 8/27 binary64))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) #s(literal -4/9 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal -2/3 binary64)))) |
(/.f64 (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64))) (-.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64)) #s(literal 8/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) (-.f64 #s(literal 4/9 binary64) (*.f64 (*.f64 x x) #s(literal 34/135 binary64)))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 289/2025 binary64) #s(literal -4/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal -2/3 binary64)))) |
(*.f64 eps #s(literal 1/3 binary64)) |
(*.f64 #s(literal 1/3 binary64) eps) |
(+.f64 (*.f64 x eps) (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps))) |
(+.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 x eps)) |
(fma.f64 x eps (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps))) |
(fma.f64 eps x (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps))) |
(fma.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (*.f64 x eps)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 eps eps) (*.f64 x eps)) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x eps)) |
(fma.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) eps (*.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 x eps) #s(literal 3 binary64))) (fma.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (-.f64 (*.f64 (*.f64 x eps) (*.f64 x eps)) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 x eps))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps))) (*.f64 (*.f64 x eps) (*.f64 x eps))) (-.f64 (*.f64 eps (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 x eps))) |
(/.f64 (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (*.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)))) |
(/.f64 (*.f64 eps (*.f64 (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) (-.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) x))) (-.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) x)) |
(/.f64 (*.f64 (fma.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (*.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 x (*.f64 x x))) eps) (fma.f64 x (-.f64 x (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) (*.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) (-.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) x)) eps) (-.f64 (fma.f64 eps (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps) x)) |
(*.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) eps) |
(*.f64 x #s(literal 2/15 binary64)) |
(*.f64 #s(literal 2/15 binary64) x) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
(*.f64 x (*.f64 x x)) |
(*.f64 (*.f64 x x) x) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
Compiled 37 868 to 2 074 computations (94.5% saved)
20 alts after pruning (15 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 984 | 12 | 996 |
| Fresh | 7 | 3 | 10 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 1 | 1 |
| Total | 992 | 20 | 1 012 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ✓ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
| 61.6% | (-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| 99.4% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.3% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| ✓ | 99.3% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
| 99.2% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| ✓ | 99.0% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 100.0% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| 99.0% | #s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(approx (pow (tan x) 2) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) | |
| ✓ | 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) | |
| 36.3% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
Compiled 1 802 to 546 computations (69.7% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.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 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.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 -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
3 calls:
| 18.0ms | x |
| 14.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 14.0ms | 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 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (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)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(approx (pow (tan x) 2) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(approx (pow (tan x) 2) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 15.0ms | eps |
| 12.0ms | x |
| 12.0ms | (-.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 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (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)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (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)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 14.0ms | eps |
| 13.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 11.0ms | 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 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 39.0ms | x |
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | x |
| 10.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 (*.f64 x #s(literal 4/3 binary64)) (+.f64 x eps) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 16.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | eps |
| 9.0ms | 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 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 11.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | eps |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
3 calls:
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
| 99.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (fma.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 (-.f64 (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) eps)) #s(literal -1/3 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 (-.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) x) (/.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) eps)) (neg.f64 eps)) (fma.f64 x (*.f64 x #s(literal -4/3 binary64)) #s(literal -1/3 binary64)))))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 eps (/.f64 x eps) eps))) #s(approx (/ 1 (/ 1 (tan x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (tan x)) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
3 calls:
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 7.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
| 99.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (*.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
3 calls:
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
| 99.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(approx (+ (* (* x x) 17/45) 2/3) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) #s(approx (* eps (+ (* eps (+ (* 4/3 (* x x)) 1)) x)) (*.f64 eps (+.f64 x eps)))) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (+ (* x (* x (* (* eps eps) 4/3))) (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)))) (+ (* (* eps eps) (* eps 1/3)) eps)) (fma.f64 eps (fma.f64 x x (*.f64 eps (fma.f64 x (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) x))) eps)))) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
3 calls:
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
Total -0.7b remaining (-111%)
Threshold costs -0.7b (-111%)
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos 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))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
3 calls:
| 5.0ms | x |
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | 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 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 24× | *-commutative_binary64 |
| 4× | +-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 132 | 773 |
| 1 | 149 | 773 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(approx (pow (tan x) 2) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| Outputs |
|---|
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(approx (pow (tan x) 2) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 277/1008 binary64)) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64))) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 eps #s(approx (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3)) #s(literal 1/3 binary64)) (/.f64 #s(approx (+ (* (sin x) (pow (tan x) 2)) (sin x)) (fma.f64 x (*.f64 (*.f64 x x) #s(literal 5/6 binary64)) x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (pow (tan (+ x eps)) 2) (pow (tan x) 2)) (+ (tan (+ x eps)) (tan x))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 9 912× | lower-fma.f64 |
| 9 912× | lower-fma.f32 |
| 9 728× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 438 |
| 0 | 104 | 411 |
| 1 | 471 | 305 |
| 2 | 4248 | 297 |
| 0 | 8129 | 287 |
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 0 | 733 | 17606 |
| 1 | 2396 | 16946 |
| 0 | 8153 | 16148 |
| 0 | 112 | 887 |
| 0 | 159 | 854 |
| 1 | 863 | 718 |
| 0 | 8356 | 690 |
| 0 | 679 | 12664 |
| 1 | 2100 | 12157 |
| 2 | 7033 | 12063 |
| 0 | 8080 | 11661 |
| 0 | 97 | 874 |
| 0 | 164 | 872 |
| 1 | 756 | 620 |
| 2 | 7370 | 620 |
| 0 | 8268 | 615 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 0 | 1088 | 22971 |
| 1 | 3518 | 22200 |
| 0 | 8478 | 21328 |
| 1× | fuel |
| 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 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 687 to 288 computations (58.1% saved)
Compiled 658 to 212 computations (67.8% saved)
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