
Time bar (total: 15.1s)
| 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)
| 3.7s | 25 887× | 0 | invalid |
| 547.0ms | 5 461× | 0 | valid |
| 533.0ms | 2 795× | 1 | valid |
ival-tan: 794.0ms (22.9% of total)const: 794.0ms (22.9% of total)ival-mult: 418.0ms (12% of total)ival-sub: 378.0ms (10.9% of total)ival-add: 238.0ms (6.9% of total)ival-<=: 220.0ms (6.3% of total)ival-fabs: 215.0ms (6.2% of total)ival-<: 186.0ms (5.4% of total)ival-and: 99.0ms (2.9% of total)adjust: 73.0ms (2.1% of total)exact: 45.0ms (1.3% of total)ival-assert: 12.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 225 | 3 | (-2.180225192017221e-32 1.1801356642024007e-34) | 4 | (1.8475405530303194e-81 2.3081092909645234e-83) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2 | 0 | - | 1 | (66.36779681348933 2.559904342158642e-12) | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | cancellation | 224 | 11 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 1 | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 222 | 4 |
| - | 3 | 27 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 222 | 4 | 0 |
| - | 3 | 7 | 20 |
| number | freq |
|---|---|
| 0 | 31 |
| 1 | 225 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 20.0ms | 178× | 1 | valid |
| 15.0ms | 334× | 0 | valid |
Compiled 49 to 22 computations (55.1% saved)
ival-tan: 12.0ms (55.1% of total)adjust: 4.0ms (18.4% of total)ival-sub: 3.0ms (13.8% of total)ival-add: 3.0ms (13.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 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 | 0.06702674348194385 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 24.076426715547658 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 9.0ms | 89× | 1 | valid |
| 8.0ms | 167× | 0 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 4.0ms (43.8% of total)adjust: 2.0ms (21.9% of total)ival-add: 2.0ms (21.9% of total)ival-sub: 1.0ms (10.9% of total)ival-true: 0.0ms (0% of total)ival-assert: 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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (sin.f64 x) (cos.f64 x)))) (-.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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(* 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 983 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 |
|---|---|---|
| 62.4% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ▶ | 62.3% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
| 62.4% | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 62.4% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) | |
| 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 62.4% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 62.3% | (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 33.6% | (-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| ▶ | 36.6% | (-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #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 (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))) | |
| ▶ | 61.5% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
| 20.2% | (-.f64 (tan.f64 (*.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)))) (tan.f64 x)) | |
| 98.7% | #s(approx (- (tan (+ x eps)) (tan x)) (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)))) | |
| 99.6% | #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)) | |
| ▶ | 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
| 98.2% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
Compiled 895 to 438 computations (51.1% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| 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 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) | |
| cost-diff | 0 | #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)) | |
| cost-diff | 0 | (neg.f64 (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 128 | (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) | |
| cost-diff | 192 | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| cost-diff | 0 | (*.f64 (+.f64 x eps) (-.f64 x eps)) | |
| cost-diff | 0 | (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) | |
| cost-diff | 0 | (-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) | |
| cost-diff | 1408 | (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) | |
| cost-diff | 0 | #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.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 (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 #s(literal 1/6 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)))) | |
| cost-diff | 5824 | (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))) (+.f64 #s(literal 1/6 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 (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)))) | |
| 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))) |
| 21 786× | lower-fma.f32 |
| 21 770× | lower-fma.f64 |
| 4 032× | lower-*.f32 |
| 4 026× | lower-*.f64 |
| 2 238× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 52 | 712 |
| 0 | 97 | 688 |
| 1 | 170 | 604 |
| 2 | 378 | 600 |
| 3 | 998 | 600 |
| 4 | 3521 | 600 |
| 5 | 6584 | 600 |
| 0 | 8179 | 590 |
| 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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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) |
(+.f64 #s(literal 1/6 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) |
(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 (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) |
(/.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 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
#s(literal 1/3 binary64) |
(*.f64 x x) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(-.f64 x eps) |
(tan.f64 x) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(sin.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
#s(literal 1 binary64) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x 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)) |
(fma.f64 eps (/.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) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (cos.f64 x))))) eps)) |
(fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 (+.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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (cos.f64 x))))) eps) |
eps |
(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))) (+.f64 #s(literal 1/6 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 (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 (+.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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (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))) (+.f64 #s(literal 1/6 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 (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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) (/.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 (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 #s(literal 1/6 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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) |
(/.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) |
(+.f64 #s(literal 1/6 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)))) |
(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)) |
#s(literal 1/6 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))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(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) |
(/.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 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
#s(literal 1/3 binary64) |
(*.f64 x x) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(+.f64 x eps) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(-.f64 x eps) |
(tan.f64 x) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(sin.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
#s(literal 1 binary64) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x 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 (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (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) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.01171875 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.015625 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.4958388018663602 | #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)) | |
| accuracy | 0 | (neg.f64 (cos.f64 x)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.06702674348194385 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 24.083070653956042 | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| accuracy | 0 | (tan.f64 x) | |
| accuracy | 0.06702674348194385 | (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) | |
| accuracy | 24.076426715547658 | (-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) | |
| accuracy | 26.01819885851174 | (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) | |
| accuracy | 0.06702674348194385 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.1875 | (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) | |
| accuracy | 0.8358091471310745 | #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) | |
| accuracy | 24.076426715547658 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) | |
| accuracy | 0.033535009768442016 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.140625 | (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))) (+.f64 #s(literal 1/6 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 (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 | 0.1571620981522978 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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)) | |
| accuracy | 0.990566259768442 | (+.f64 #s(literal 1/6 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)))) |
| 97.0ms | 95× | 1 | valid |
| 64.0ms | 159× | 0 | valid |
| 2.0ms | 1× | 3 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 628 to 55 computations (91.2% saved)
ival-pow2: 26.0ms (20% of total)ival-mult: 20.0ms (15.3% of total)ival-add: 17.0ms (13% of total)ival-div: 14.0ms (10.7% of total)adjust: 12.0ms (9.2% of total)ival-pow: 11.0ms (8.4% of total)const: 8.0ms (6.1% of total)ival-tan: 7.0ms (5.4% of total)ival-sub: 5.0ms (3.8% of total)ival-cos: 3.0ms (2.3% of total)ival-neg: 3.0ms (2.3% of total)ival-sin: 2.0ms (1.5% of total)exact: 1.0ms (0.8% 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 (-.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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 (+.f64 #s(literal 1/6 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)))) (patch (+.f64 #s(literal 1/6 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)))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) (patch (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.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 (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) (patch #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) (patch (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) (patch (-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) #<representation binary64>) () ()) |
#s(alt (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (patch (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) #<representation binary64>) () ()) |
#s(alt (*.f64 (+.f64 x eps) (-.f64 x eps)) (patch (*.f64 (+.f64 x eps) (-.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) (patch (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) #<representation binary64>) () ()) |
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ()) |
#s(alt (neg.f64 (cos.f64 x)) (patch (neg.f64 (cos.f64 x)) #<representation binary64>) () ()) |
#s(alt #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)) (patch #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)) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (patch (fma.f64 eps (/.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 (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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ()) |
#s(alt (cos.f64 x) (patch (cos.f64 x) #<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>) () ()) |
| 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 (- (+ (* -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 (* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) (taylor 0 x) (#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 (sin x) 4) (taylor inf x) (#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 (sin x) 4) (taylor inf x) (#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 (sin x) 4) (taylor inf x) (#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 (sin x) 4) (taylor inf x) (#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 (sin x) 4) (taylor -inf x) (#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 (sin x) 4) (taylor -inf x) (#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 (sin x) 4) (taylor -inf x) (#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 (sin x) 4) (taylor -inf x) (#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 (* 1/3 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #<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>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#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 (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#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 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) (taylor 0 x) (#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 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) (taylor 0 x) (#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 (pow (cos x) 2) (taylor inf x) (#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 (pow (cos x) 2) (taylor inf x) (#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 (pow (cos x) 2) (taylor inf x) (#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 (pow (cos x) 2) (taylor inf x) (#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 (pow (cos x) 2) (taylor -inf x) (#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 (pow (cos x) 2) (taylor -inf x) (#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 (pow (cos x) 2) (taylor -inf x) (#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 (pow (cos x) 2) (taylor -inf x) (#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
111 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 9.0ms | x | @ | inf | (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
| 4.0ms | x | @ | -inf | (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
| 3.0ms | x | @ | inf | (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)) |
| 2.0ms | eps | @ | 0 | (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
| 1.0ms | x | @ | -inf | (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)) |
| 1× | egg-herbie |
| 9 598× | lower-fma.f64 |
| 9 598× | lower-fma.f32 |
| 6 030× | lower-*.f64 |
| 6 030× | lower-*.f32 |
| 3 110× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 459 | 7572 |
| 1 | 1345 | 7214 |
| 2 | 4084 | 6646 |
| 0 | 8100 | 6351 |
| 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) |
(/ (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 |
(- (* -1/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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(/ (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 (* -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)) |
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))) |
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(* -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))) |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (sin eps) (cos eps)) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
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(/ (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)))) |
(* -1 (pow eps 2)) |
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(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) |
(pow x 2) |
(+ (* eps (+ x (* -1 x))) (pow x 2)) |
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) |
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) |
(* -1 (pow eps 2)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ x eps)) 1)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1)) |
(* -1 (pow eps 2)) |
(* (pow eps 2) (- (* -1 (/ (+ x (* -1 x)) eps)) 1)) |
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1)) |
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1)) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
(/ -1 (cos x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
-1 |
(- (* 1/2 (pow x 2)) 1) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos x)) |
(* -1 (cos 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 (/ (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))) |
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))) |
(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 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) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
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 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos 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) |
| 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 x (*.f64 x (fma.f64 x (*.f64 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)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (+.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))) #s(literal 4/3 binary64)))) (*.f64 eps eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (+.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))) #s(literal 4/3 binary64)))) (*.f64 eps eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) |
(* (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)))))) |
(*.f64 eps (*.f64 eps (+.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))) #s(literal 4/3 binary64)))))) |
(* (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)))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
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-1/3 |
#s(literal -1/3 binary64) |
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos 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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(-.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))))) |
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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))) |
(/ (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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 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 (fma.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))) (neg.f64 (+.f64 (fma.f64 #s(literal -1/2 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)))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 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)))) (/.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))))) |
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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))) |
(/ (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))) |
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(+ (* 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))) |
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
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(+.f64 x eps) |
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(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
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) |
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(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(+ eps x) |
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(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
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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 |
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(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x 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 x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
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(+ eps x) |
(+.f64 x eps) |
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) |
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(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
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(+ eps x) |
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(+ eps x) |
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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 |
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(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
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(fma.f64 eps (/.f64 x eps) eps) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
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(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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(-.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 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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))))) |
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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))) |
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(/ -1 (cos x)) |
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(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 x (*.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) x) |
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(sin.f64 x) |
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(sin x) |
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(sin x) |
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(sin x) |
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(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
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#s(literal -1 binary64) |
(- (* 1/2 (pow x 2)) 1) |
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
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(* -1 (cos x)) |
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(* -1 (cos x)) |
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(* -1 (cos x)) |
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(* -1 (cos x)) |
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(* -1 (cos x)) |
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(/.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))) |
(-.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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(-.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 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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))))) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 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 (- (+ 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 (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)))) |
(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) |
(* -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) |
(* -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) |
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 (*.f64 x 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)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 eps #s(literal 32/45 binary64) (*.f64 #s(literal -1/3 binary64) eps)) (*.f64 eps #s(literal 2/3 binary64))) eps) 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) |
(+ 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) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) |
(* (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)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(*.f64 x (fma.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 x x)) x x)) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(*.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))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/315 binary64) #s(literal 2/45 binary64))) #s(literal -1/3 binary64))) x)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow x 4) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -2/3 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5 binary64)) #s(literal -2/3 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -34/945 binary64) #s(literal 1/5 binary64)) #s(literal -2/3 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(* 1/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
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 x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x) |
(* 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 x (*.f64 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)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
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 x (*.f64 x #s(literal 1/3 binary64)) #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)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
| 4 106× | lower-fma.f32 |
| 4 090× | lower-fma.f64 |
| 4 002× | lower-*.f32 |
| 3 996× | lower-*.f64 |
| 2 940× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 52 | 368 |
| 0 | 97 | 339 |
| 1 | 432 | 241 |
| 2 | 3951 | 237 |
| 0 | 8143 | 229 |
| 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 (-.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))) (+.f64 #s(literal 1/6 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 (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)))) |
(+.f64 #s(literal 1/6 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(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
(sin.f64 x) |
(neg.f64 (cos.f64 x)) |
#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)) |
(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)) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(tan.f64 x) |
(cos.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
| 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(+.f64 (*.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))))) |
(+.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) |
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 #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 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 -1/2 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 #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 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))))) |
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(*.f64 (-.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))))) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (sin.f64 x)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 4 binary64))) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 x #s(literal 1/3 binary64)) x) |
(exp.f64 (log.f64 (tan.f64 x))) |
(tan.f64 x) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (sin.f64 x))) |
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x))) |
(pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal -1 binary64)) |
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(exp.f64 (log.f64 (cos.f64 x))) |
(cos.f64 x) |
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x))) |
(neg.f64 (neg.f64 (cos.f64 x))) |
(pow.f64 (cos.f64 x) #s(literal 1 binary64)) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))) |
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x))) |
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x)))) |
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))) #s(literal 1 binary64))) |
(exp.f64 (+.f64 (log.f64 (cos.f64 x)) (log.f64 (cos.f64 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) (cos.f64 (-.f64 x x))) #s(literal 2 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 x))) |
(*.f64 (cos.f64 x) (cos.f64 x)) |
(*.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 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 2 binary64))) |
Compiled 89 966 to 4 911 computations (94.5% saved)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 812 | 14 | 1 826 |
| Fresh | 9 | 4 | 13 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 826 | 19 | 1 845 |
| Status | Accuracy | Program |
|---|---|---|
| 62.4% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) | |
| ▶ | 62.4% | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
| 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 62.4% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| ▶ | 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
| 52.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) eps)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) eps)) | |
| ▶ | 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
| 99.6% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) eps)) | |
| 98.7% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| 98.1% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) | |
| 98.2% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) | |
| 34.5% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64)))))) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) | |
| ▶ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
Compiled 741 to 374 computations (49.5% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (-.f64 (+.f64 x eps) x)) | |
| cost-diff | 0 | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| cost-diff | 384 | (-.f64 (+.f64 x eps) x) | |
| cost-diff | 0 | #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) | |
| cost-diff | 0 | (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) | |
| cost-diff | 0 | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) | |
| 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))) |
| 12 900× | lower-fma.f32 |
| 12 882× | lower-fma.f64 |
| 4 704× | lower-+.f32 |
| 4 696× | lower-+.f64 |
| 4 242× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 615 |
| 0 | 113 | 598 |
| 1 | 198 | 596 |
| 2 | 379 | 591 |
| 3 | 842 | 575 |
| 4 | 2136 | 575 |
| 5 | 7943 | 575 |
| 0 | 8372 | 547 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
eps |
(fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) |
eps |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) |
x |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(*.f64 x x) |
#s(literal 2/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) |
(*.f64 x x) |
#s(literal 2/15 binary64) |
#s(literal 1/3 binary64) |
(*.f64 x (*.f64 x x)) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(sin.f64 (-.f64 (+.f64 x eps) x)) |
(-.f64 (+.f64 x eps) x) |
(+.f64 x eps) |
x |
eps |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(cos.f64 x) |
(cos.f64 (+.f64 x eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.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 (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))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (/.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 (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))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
eps |
(fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (fma.f64 eps (/.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 (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))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(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 eps (/.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 (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 (+.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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) |
eps |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) |
x |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(*.f64 x x) |
#s(literal 2/3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) |
(*.f64 x x) |
#s(literal 2/15 binary64) |
#s(literal 1/3 binary64) |
(*.f64 x (*.f64 x x)) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(sin.f64 (-.f64 (+.f64 x eps) x)) |
(sin.f64 eps) |
(-.f64 (+.f64 x eps) x) |
eps |
(+.f64 x eps) |
x |
eps |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(cos.f64 x) |
(cos.f64 (+.f64 x eps)) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) | |
| accuracy | 0.01171875 | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| accuracy | 0.03304465476030194 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 24.074549655389642 | (-.f64 (+.f64 x eps) x) | |
| accuracy | 0.06702674348194385 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.0859375 | (*.f64 x (*.f64 x x)) | |
| accuracy | 0.7884909777356495 | #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| accuracy | 24.076426715547658 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| accuracy | 0.01171875 | (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) | |
| accuracy | 0.203125 | (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) | |
| accuracy | 0.4958388018663602 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) | |
| accuracy | 0.8349185007498844 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) | |
| accuracy | 60.6154837574342 | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) | |
| accuracy | 0.12109375 | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) | |
| accuracy | 0.140625 | (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.1571620981522978 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| accuracy | 32.37868338463354 | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| 297.0ms | 246× | 1 | valid |
| 4.0ms | 8× | 0 | valid |
| 3.0ms | 1× | 3 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 506 to 64 computations (87.4% saved)
ival-cos: 51.0ms (19.7% of total)ival-add: 44.0ms (17% of total)ival-mult: 43.0ms (16.6% of total)adjust: 35.0ms (13.5% of total)ival-pow2: 27.0ms (10.4% of total)const: 22.0ms (8.5% of total)ival-div: 15.0ms (5.8% of total)ival-sub: 7.0ms (2.7% of total)ival-tan: 7.0ms (2.7% of total)ival-sin: 5.0ms (1.9% of total)ival-neg: 2.0ms (0.8% of total)exact: 1.0ms (0.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) (patch #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) (patch (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) (patch #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) #<representation binary64>) () ()) |
#s(alt (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) (patch (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) (patch #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 x eps) x) (patch (-.f64 (+.f64 x eps) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ()) |
#s(alt (sin.f64 (-.f64 (+.f64 x eps) x)) (patch (sin.f64 (-.f64 (+.f64 x eps) x)) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 (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))) eps (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 x x) #s(literal 2/3 binary64)) (patch (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 x (*.f64 x x)) (patch (*.f64 x (*.f64 x x)) #<representation binary64>) () ()) |
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.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>) () ())) ()) |
#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>) () ())) ()) |
#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>) () ())) ()) |
#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))))))))) (taylor inf 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)))))) (+ (/ (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))))))))) (taylor inf 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)))))) (+ (/ (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))))))))) (taylor inf 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)))))) (+ (/ (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))))))))) (taylor inf 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 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos eps) (taylor 0 x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) (taylor 0 x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) (taylor 0 x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (pow (cos x) 2) (taylor 0 eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
#s(alt (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ()) |
111 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 11.0ms | x | @ | inf | (cos (+ x eps)) |
| 8.0ms | eps | @ | 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))) |
| 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))) |
| 4.0ms | eps | @ | 0 | (+ (* 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))) |
| 1× | egg-herbie |
| 8 702× | lower-fma.f64 |
| 8 702× | lower-fma.f32 |
| 7 288× | lower-*.f64 |
| 7 288× | lower-*.f32 |
| 2 808× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 544 | 9119 |
| 1 | 1711 | 8503 |
| 2 | 5157 | 8205 |
| 0 | 8864 | 7855 |
| 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))) |
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(- (/ (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 (/ (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)))) |
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(* -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))) |
eps |
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(+ 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))) |
(+ eps (/ (* eps (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 (* (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 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* 2/3 (pow x 4)) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(* 2/3 (pow x 4)) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(/ (sin eps) (cos eps)) |
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(- (/ (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))))) |
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(- (/ (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))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (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))) |
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(* -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)) |
eps |
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eps |
eps |
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eps |
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eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(/ (sin eps) (cos eps)) |
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(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
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(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 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))) |
(/ (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)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(* 2/3 (pow x 2)) |
(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) |
(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))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(pow (cos x) 2) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (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)) (pow.f64 (/.f64 (sin.f64 x) (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 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (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 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (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 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (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))))))))) |
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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))))) |
(fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (*.f64 eps #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)))) |
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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 |
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(fma.f64 x (fma.f64 x (fma.f64 (+.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)) #s(literal 1/6 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)))) (neg.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))) (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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (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)) #s(literal 1 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))))) |
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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 (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)))) |
(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) |
(* -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) |
(* -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) |
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 eps (*.f64 (*.f64 x x) #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)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 eps #s(literal 2/45 binary64) (fma.f64 eps #s(literal -1/3 binary64) (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps #s(literal 2/3 binary64))) eps) 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) |
(+ 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) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x 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 x (*.f64 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)))))))) |
(*.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))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)))) |
(* 2/3 (pow x 4)) |
(*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* 2/3 (pow x 4)) |
(*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 2/3 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (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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(* eps (- 1 (* -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))) |
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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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(-.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))) |
(- (/ (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))) |
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(/ (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))) |
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eps |
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(+.f64 x eps) |
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(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
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) |
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(fma.f64 x (/.f64 eps x) x) |
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(fma.f64 x (/.f64 eps x) x) |
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(fma.f64 x (/.f64 eps x) x) |
x |
(+ eps x) |
(+.f64 x eps) |
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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 |
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(fma.f64 eps (/.f64 x eps) eps) |
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(fma.f64 eps (/.f64 x eps) eps) |
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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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(sin eps) |
(sin.f64 eps) |
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(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
eps |
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
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(sin eps) |
(sin.f64 eps) |
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(sin.f64 eps) |
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(sin.f64 eps) |
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(-.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))) |
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(- (/ (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))))) |
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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))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 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 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 eps (*.f64 eps #s(literal 1/3 binary64))) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
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(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
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(+ (* 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 (+.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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (- (+ 1/3 (+ (* 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 (+.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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (- (+ 1/3 (+ (* 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))) |
(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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (- (+ 1/3 (+ (* 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))) |
(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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (- (+ 1/3 (+ (* 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))) |
(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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (- (+ 1/3 (+ (* 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))) |
(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 (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 -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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)))) |
(pow x 4) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/5 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 92/945 binary64) #s(literal 1/5 binary64)) #s(literal 1/3 binary64)) #s(literal 1 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(* 2/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 2/3 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)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 x (-.f64 (*.f64 x (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (sin.f64 eps)) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (sin.f64 eps) #s(literal 1/6 binary64)) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 eps (-.f64 (*.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 eps (-.f64 (*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))) (sin.f64 x)) (cos.f64 x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(fma.f64 x (neg.f64 (fma.f64 x (cos.f64 eps) (sin.f64 eps))) (cos.f64 eps)) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(fma.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 x (*.f64 (sin.f64 eps) #s(literal 2/3 binary64))) (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps)) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(fma.f64 (*.f64 (cos.f64 x) eps) (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(fma.f64 eps (fma.f64 (sin.f64 x) (neg.f64 (cos.f64 x)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
| 4 798× | lower-fma.f32 |
| 4 780× | lower-fma.f64 |
| 4 182× | lower-*.f32 |
| 4 168× | lower-*.f64 |
| 2 946× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 385 |
| 0 | 113 | 370 |
| 1 | 479 | 311 |
| 2 | 3862 | 311 |
| 0 | 8184 | 307 |
| 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (+.f64 x eps) x) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(sin.f64 (-.f64 (+.f64 x eps) x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(*.f64 x (*.f64 x x)) |
(cos.f64 (+.f64 x eps)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
| Outputs |
|---|
(+.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 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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)))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))) eps (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 #s(literal 1 binary64) (/.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 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 #s(literal -1 binary64) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) #s(literal -1 binary64)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) #s(literal -1 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 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) |
(fma.f64 (pow.f64 (/.f64 (cos.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)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (-.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 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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))))) (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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)))) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (-.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 2 binary64))))) |
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(pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 2 binary64))))) |
(*.f64 (-.f64 (pow.f64 (*.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (sin.f64 x) (tan.f64 x))))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (sin.f64 x) (tan.f64 x)))) #s(literal 1 binary64))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (sin.f64 x) (tan.f64 x)))) |
(*.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 2 binary64))) |
(*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(*.f64 (tan.f64 x) (*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (tan.f64 x)))) |
(*.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (*.f64 (sin.f64 x) (tan.f64 x))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) |
(*.f64 (*.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (sin.f64 x)) (tan.f64 x)) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (tan.f64 x)) (tan.f64 x)) |
(*.f64 x (*.f64 x #s(literal 2/3 binary64))) |
(*.f64 (*.f64 x x) #s(literal 2/3 binary64)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x #s(literal 2/3 binary64)) x) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.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))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(cos.f64 (+.f64 eps x)) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (-.f64 #s(literal 0 binary64) eps))))) |
(/.f64 (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (-.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(/.f64 (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (+.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (-.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (-.f64 #s(literal 0 binary64) eps)))) #s(literal -1 binary64)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(*.f64 (+.f64 (cos.f64 (+.f64 eps (+.f64 x x))) (cos.f64 (-.f64 #s(literal 0 binary64) eps))) #s(literal 1/2 binary64)) |
Compiled 34 589 to 2 335 computations (93.2% saved)
22 alts after pruning (18 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 872 | 11 | 883 |
| Fresh | 6 | 7 | 13 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 880 | 22 | 902 |
| Status | Accuracy | Program |
|---|---|---|
| 62.4% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) | |
| ▶ | 99.9% | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
| 99.8% | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 99.9% | (/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 62.4% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ✓ | 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x))) |
| ▶ | 99.9% | (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
| 99.6% | #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| 99.2% | #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| ▶ | 99.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) eps)) | |
| ✓ | 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
| ▶ | 98.7% | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
| 98.2% | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps)) | |
| 98.1% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) | |
| ▶ | 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
| ✓ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
Compiled 691 to 382 computations (44.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) | |
| cost-diff | 0 | #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) | |
| cost-diff | 0 | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| cost-diff | 0 | #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)) | |
| cost-diff | 0 | (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) | |
| cost-diff | 0 | #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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) | |
| cost-diff | 0 | (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) | |
| cost-diff | 0 | (*.f64 x eps) | |
| cost-diff | 0 | (fma.f64 x (*.f64 x eps) eps) | |
| cost-diff | 0 | #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) | |
| cost-diff | 0 | (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) | |
| cost-diff | 192 | (+.f64 eps #s(literal 0 binary64)) | |
| cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
| 11 550× | lower-fma.f32 |
| 11 528× | lower-fma.f64 |
| 3 506× | lower-+.f32 |
| 3 500× | lower-+.f64 |
| 3 498× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 83 | 780 |
| 0 | 127 | 766 |
| 1 | 245 | 757 |
| 2 | 650 | 749 |
| 3 | 1731 | 714 |
| 4 | 2822 | 714 |
| 5 | 6270 | 714 |
| 0 | 8275 | 681 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
#s(literal 1 binary64) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(cos.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(sin.f64 (+.f64 eps #s(literal 0 binary64))) |
(+.f64 eps #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) |
(fma.f64 x (*.f64 x eps) eps) |
x |
(*.f64 x eps) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
(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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) |
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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
x |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal 4/3 binary64)) |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
eps |
(fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
#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)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
#s(literal 1/3 binary64) |
x |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) |
(fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(*.f64 eps eps) |
eps |
(fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 eps (*.f64 eps eps)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(cos.f64 x) |
x |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(literal 1 binary64) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(cos.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
eps |
(sin.f64 (+.f64 eps #s(literal 0 binary64))) |
(sin.f64 eps) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) |
(fma.f64 x (*.f64 x eps) eps) |
x |
(*.f64 x eps) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (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)) |
(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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) |
(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))) eps) (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 (+ (* (+ (* 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
#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))) eps) (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)))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
(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))) |
x |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 eps #s(literal 4/3 binary64)) |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 eps #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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)) |
(fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps (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 |
(fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(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))) |
#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)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
#s(literal 1/3 binary64) |
x |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) |
#s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) |
(fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(*.f64 eps eps) |
eps |
(fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 eps (*.f64 eps eps)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(cos.f64 x) |
x |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| accuracy | 0.026591230164287515 | #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) | |
| accuracy | 0.03304465476030194 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 0.0859375 | (*.f64 eps (*.f64 eps eps)) | |
| accuracy | 0.015625 | (pow.f64 (tan.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.13671875 | (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.1571620981522978 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| accuracy | 1.256585975968938 | #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)) | |
| accuracy | 0.1571620981522978 | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) | |
| accuracy | 0.2734375 | (*.f64 eps #s(literal 1/3 binary64)) | |
| accuracy | 0.27734375 | (*.f64 eps #s(literal 4/3 binary64)) | |
| accuracy | 1.207420543389125 | #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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) | |
| accuracy | 0 | (fma.f64 x (*.f64 x eps) eps) | |
| accuracy | 0 | (*.f64 x eps) | |
| accuracy | 0.4958388018663602 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) | |
| accuracy | 0.837977213982705 | #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) | |
| accuracy | 0.00390625 | (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) | |
| accuracy | 0.0078125 | (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) | |
| accuracy | 0.015625 | (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) | |
| accuracy | 0.03304465476030194 | (cos.f64 (+.f64 eps x)) |
| 161.0ms | 89× | 1 | valid |
| 89.0ms | 165× | 0 | valid |
| 6.0ms | 2× | 5 | exit |
Compiled 542 to 80 computations (85.2% saved)
ival-pow2: 62.0ms (28.1% of total)ival-mult: 42.0ms (19.1% of total)const: 27.0ms (12.3% of total)ival-add: 26.0ms (11.8% of total)ival-cos: 22.0ms (10% of total)adjust: 16.0ms (7.3% of total)ival-div: 10.0ms (4.5% of total)ival-sub: 6.0ms (2.7% of total)ival-sin: 6.0ms (2.7% of total)ival-tan: 4.0ms (1.8% of total)exact: 1.0ms (0.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ()) |
#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ()) |
#s(alt (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (patch (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) (patch #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (*.f64 x eps) eps) (patch (fma.f64 x (*.f64 x eps) eps) #<representation binary64>) () ()) |
#s(alt (*.f64 x eps) (patch (*.f64 x eps) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) #<representation binary64>) () ()) |
#s(alt (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) (patch (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) #<representation binary64>) () ()) |
#s(alt #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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) (patch #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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (patch (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) (patch (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) #<representation binary64>) () ()) |
#s(alt (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ()) |
#s(alt #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)) (patch #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)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ()) |
#s(alt #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (patch #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) (patch (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (patch (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #<representation binary64>) () ()) |
#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt (*.f64 eps #s(literal 4/3 binary64)) (patch (*.f64 eps #s(literal 4/3 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 eps #s(literal 1/3 binary64)) (patch (*.f64 eps #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 (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ()) |
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf eps) (#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) (patch (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 eps #s(literal 0 binary64)) (patch (+.f64 eps #s(literal 0 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (cos eps)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (sin eps) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 2)))))))) (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (patch (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #<representation binary64>) () ())) ()) |
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#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor inf x) (#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 (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#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 (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#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 (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#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 (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#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 (pow eps 3) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (*.f64 eps (*.f64 eps eps)) (patch (*.f64 eps (*.f64 eps eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos eps) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
135 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | -inf | (/ 1 (* (cos x) (cos (+ eps x)))) |
| 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))) eps) (pow (tan x) 2))) 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))) eps) (pow (tan x) 2))) 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))) eps) (pow (tan x) 2))) eps) |
| 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))) eps) (pow (tan x) 2))) eps) |
| 1× | egg-herbie |
| 10 656× | lower-fma.f64 |
| 10 656× | lower-fma.f32 |
| 5 966× | lower-*.f64 |
| 5 966× | lower-*.f32 |
| 4 422× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 590 | 14038 |
| 1 | 1880 | 13738 |
| 2 | 6055 | 13318 |
| 0 | 8171 | 12679 |
| 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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(/ 1 (cos eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (/ 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) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 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 x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/ 1 (pow (cos x) 2)) |
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(pow (cos x) 2) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (+ eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 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 (/ (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))) |
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 |
(+ eps (* eps (pow x 2))) |
(+ eps (* eps (pow x 2))) |
(+ eps (* eps (pow x 2))) |
(* eps (pow x 2)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* eps (pow x 2)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps 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 (+ (* 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))) |
(* 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 (pow eps 2))))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(pow x 2) |
(+ (* eps x) (pow x 2)) |
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)) |
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (/ (sin (+ eps 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 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)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 eps))) |
(sin (neg (* -1 eps))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(* -1/5040 (pow eps 7)) |
(* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(* -1/5040 (pow eps 7)) |
(* -1 (* (pow eps 7) (- 1/5040 (* 1/120 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (* 1/120 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
-1/6 |
(- (* 1/120 (pow eps 2)) 1/6) |
(- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6) |
(- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6) |
(* -1/5040 (pow eps 4)) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(* -1/5040 (pow eps 4)) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(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))) |
(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))) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 eps) |
(* 4/3 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) |
(* 1/3 eps) |
(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 eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(pow eps 3) |
(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))) |
| 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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 x (fma.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 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 (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 x (fma.f64 x (fma.f64 (-.f64 (*.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (neg.f64 x) (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 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) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ eps (pow (cos x) 2)) |
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(fma.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(fma.f64 (fma.f64 eps (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 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 4 binary64)))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps eps) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(fma.f64 (fma.f64 eps (fma.f64 (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 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 4 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 eps) (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 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 4 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps eps) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(/ 1 (cos eps)) |
(/.f64 #s(literal 1 binary64) (cos.f64 eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(fma.f64 (sin.f64 eps) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(+ (* x (- (* x (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (sin eps) (pow (cos eps) 2))) (+ (* -1 (/ (* (sin eps) (- (/ 1 (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* 1/6 (/ (sin eps) (pow (cos eps) 2))) (* 1/2 (/ (sin eps) (pow (cos eps) 2)))))))) (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(fma.f64 x (fma.f64 x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (fma.f64 (neg.f64 x) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (neg.f64 (cos.f64 eps))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- eps (* -1 x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (pow (cos x) 2)) |
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))) |
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 #s(literal 1/2 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 4 binary64)))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (+.f64 (/.f64 #s(literal 1/2 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 4 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (/.f64 #s(literal 1/2 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 4 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (+ eps x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ 1 (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x)) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(fma.f64 x (neg.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps))) (cos.f64 eps)) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(fma.f64 x (fma.f64 x (-.f64 (*.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64)) (cos.f64 eps)) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (*.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (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 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 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 (- (* 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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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 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))) |
(fma.f64 x (fma.f64 x (fma.f64 (neg.f64 x) (+.f64 #s(literal 1/2 binary64) (-.f64 (fma.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 #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 binary64)))) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)))))) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 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))) (/ (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 (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 (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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)))))) |
(* 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 (-.f64 #s(literal -1/6 binary64) (+.f64 (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))) (*.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 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 (*.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 (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (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))) (*.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 #s(literal 1/6 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)))))) (cos.f64 x)) (*.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 #s(literal -1/6 binary64) (+.f64 (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))) (*.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 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 (*.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 #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 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))) |
(* 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)) (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 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 #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)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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 #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 (/.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 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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)))))))) |
(* (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))))))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 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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(+ (* 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 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))))))))) |
(*.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)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 eps eps)) |
(* (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))))))))) |
(*.f64 (*.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 (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 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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))))))))) |
(*.f64 (*.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 (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 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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))))))))) |
(*.f64 (+.f64 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 eps eps)) |
(* (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))))))))) |
(*.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)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 eps eps)) |
(* (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))))))))) |
(*.f64 (*.f64 eps eps) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (+.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)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) 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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(fma.f64 eps x (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 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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(-.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 (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 (/.f64 (*.f64 (sin.f64 x) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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)))))) |
(* 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 (-.f64 #s(literal -1/6 binary64) (+.f64 (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))) (*.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 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 (*.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 (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (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))) (*.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 #s(literal 1/6 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)))))) (cos.f64 x)) (*.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 #s(literal -1/6 binary64) (+.f64 (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))) (*.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 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 (*.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 #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 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))) |
(* 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)) (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (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 (+ (* 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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 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 #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)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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 #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 (/.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 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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)))))))) |
(* (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 #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 (/.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 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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)))))))) |
(* (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 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 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))))) |
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(* -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))))) |
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(fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (-.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 (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 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 (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)))) |
(* (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))))))))) |
(*.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)))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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 eps eps)) |
(* (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))))))))) |
(*.f64 (*.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 (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 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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))))))))) |
(*.f64 (*.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 (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 (/.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal 1 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))))))) |
(* (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 eps x (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 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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(+ (* 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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(+ (* 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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(* 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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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
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(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) eps) |
(* -1/5040 (pow eps 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 eps #s(literal 7 binary64))) |
(* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps)))) |
(* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* (pow eps 7) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) |
(* -1/5040 (pow eps 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 eps #s(literal 7 binary64))) |
(* -1 (* (pow eps 7) (- 1/5040 (* 1/120 (/ 1 (pow eps 2)))))) |
(*.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (neg.f64 (pow.f64 eps #s(literal 7 binary64)))) |
(* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (* 1/120 (/ 1 (pow eps 2)))))) |
(neg.f64 (*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (/.f64 #s(literal -1/120 binary64) (*.f64 eps eps)))))) |
(* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(*.f64 (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (-.f64 (/.f64 #s(literal -1/120 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))))) (neg.f64 (pow.f64 eps #s(literal 7 binary64)))) |
-1/6 |
#s(literal -1/6 binary64) |
(- (* 1/120 (pow eps 2)) 1/6) |
(fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) |
(- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(* -1/5040 (pow eps 4)) |
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* -1/5040 (pow eps 4)) |
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 eps (-.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))) (cos.f64 x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 x (fma.f64 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x))) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 binary64)) |
(* 4/3 eps) |
(*.f64 eps #s(literal 4/3 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)) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 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 x (*.f64 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)))))))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 x (fma.f64 (cos.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x))) (sin.f64 (neg.f64 eps))) (cos.f64 eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 eps (-.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))) (cos.f64 x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
| 306× | lower-*.f32 |
| 290× | lower-*.f64 |
| 230× | lower-+.f32 |
| 224× | lower-+.f64 |
| 192× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 83 | 704 |
| 0 | 127 | 692 |
| 0 | 622 | 659 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(+.f64 eps #s(literal 0 binary64)) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) |
(fma.f64 x (*.f64 x eps) eps) |
(*.f64 x eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
(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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
#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)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) |
(fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(cos.f64 (+.f64 eps x)) |
(*.f64 eps #s(literal 4/3 binary64)) |
(*.f64 eps #s(literal 1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(*.f64 eps (*.f64 eps eps)) |
(cos.f64 (+.f64 x eps)) |
| Outputs |
|---|
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (sin.f64 eps)) |
(*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
eps |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (fma.f64 eps (*.f64 eps eps) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64))))) |
(/.f64 (-.f64 (*.f64 eps eps) #s(literal 0 binary64)) (-.f64 eps #s(literal 0 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 (+.f64 x eps))) |
(pow.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 x eps))) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps)) |
(+.f64 eps (*.f64 (*.f64 x x) eps)) |
(+.f64 (*.f64 (*.f64 x x) eps) eps) |
(fma.f64 x (*.f64 x eps) eps) |
(fma.f64 (*.f64 x eps) x eps) |
(fma.f64 (*.f64 x x) eps eps) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) eps) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 (*.f64 x x) eps) (*.f64 (*.f64 x x) eps) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 (*.f64 x x) eps) eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) (*.f64 (*.f64 x x) eps)) (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 x x) eps) eps)) |
(*.f64 x eps) |
(*.f64 eps x) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
(+.f64 eps (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))))) |
(+.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
(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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps) |
(fma.f64 #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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps eps) |
(/.f64 (+.f64 (pow.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) (-.f64 (*.f64 eps eps) (*.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) eps)))) |
(/.f64 (-.f64 (*.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))))) (*.f64 eps eps)) (-.f64 (*.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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))) 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
(+.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
(fma.f64 eps (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
(fma.f64 (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
(fma.f64 (*.f64 eps #s(literal 1/3 binary64)) eps (*.f64 x (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 1/3 binary64) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) #s(literal 3 binary64))) (fma.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (-.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (*.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) (-.f64 (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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)) |
(+.f64 eps (*.f64 eps (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))))) |
(+.f64 (*.f64 eps (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) |
(fma.f64 eps (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) |
(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 (+.f64 (pow.f64 (*.f64 eps (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)))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (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)))) (*.f64 eps (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)))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (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)))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (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)))) (*.f64 eps (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))))) (*.f64 eps eps)) (-.f64 (*.f64 eps (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)) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.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)))) |
(+.f64 (*.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))) |
(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))) |
(fma.f64 (tan.f64 x) (tan.f64 x) (*.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)))) |
(fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (*.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)))) |
(/.f64 (+.f64 (pow.f64 (*.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))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.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))) (*.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))) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (*.f64 (*.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)))))) |
(/.f64 (-.f64 (*.f64 (*.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))) (*.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)))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (*.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)))) |
#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)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 (neg.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps))) (neg.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps))) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
#s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) |
(+.f64 eps (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)))) |
(+.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) eps) |
(fma.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) eps) (*.f64 eps eps) eps) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps)) (-.f64 (*.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) eps)) |
(+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) |
(+.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) #s(literal -1/6 binary64)) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) |
(/.f64 (+.f64 (pow.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) #s(literal 3 binary64)) #s(literal -1/216 binary64)) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (-.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) #s(literal -1/6 binary64))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) #s(literal 1/36 binary64)) (-.f64 (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) #s(literal -1/6 binary64))) |
(cos.f64 (+.f64 x eps)) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(*.f64 eps #s(literal 4/3 binary64)) |
(*.f64 #s(literal 4/3 binary64) eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(*.f64 #s(literal 1/3 binary64) eps) |
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(*.f64 (tan.f64 x) (tan.f64 x)) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 1 binary64))) |
(pow.f64 eps #s(literal 3 binary64)) |
(*.f64 eps (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) eps) |
(cos.f64 (+.f64 x eps)) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
Compiled 19 000 to 763 computations (96% saved)
25 alts after pruning (19 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 612 | 10 | 622 |
| Fresh | 4 | 9 | 13 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 3 | 4 |
| Total | 619 | 25 | 644 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.9% | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
| 99.6% | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))))) | |
| 99.8% | (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 99.9% | (/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 62.4% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 62.3% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 100.0% | (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) | |
| 99.9% | (*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) | |
| 99.2% | #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) | |
| ✓ | 99.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
| 98.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) | |
| 98.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) | |
| 98.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) eps)) | |
| ✓ | 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
| 98.2% | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) eps)) | |
| 98.7% | #s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) eps)) | |
| 98.1% | #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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) | |
| ✓ | 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
| 6.3% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) | |
| ✓ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
Compiled 1 540 to 501 computations (67.5% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (tan.f64 (*.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)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))))) |
#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)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64)))))) |
#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (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))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (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))) (+.f64 #s(literal 1/6 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 (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 |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
3 calls:
| 25.0ms | eps |
| 15.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 14.0ms | x |
| 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (tan.f64 (*.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)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))))) |
#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)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
3 calls:
| 14.0ms | x |
| 14.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (tan.f64 (*.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)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
| Outputs |
|---|
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
3 calls:
| 13.0ms | eps |
| 11.0ms | (-.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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (tan.f64 (*.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)))) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 2 binary64))) eps)) |
| Outputs |
|---|
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
3 calls:
| 10.0ms | eps |
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(-.f64 (tan.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
| Outputs |
|---|
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
3 calls:
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 9.0ms | 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 #s(approx (+ (* (* eps eps) (+ (* (* eps eps) -1/5040) 1/120)) -1/6) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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 eps x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
| Outputs |
|---|
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
3 calls:
| 10.0ms | (-.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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(-.f64 (tan.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
3 calls:
| 12.0ms | (-.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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
3 calls:
| 8.0ms | eps |
| 7.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 7.0ms | x |
| 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)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (*.f64 x 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 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
3 calls:
| 7.0ms | x |
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | eps |
| 98.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 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)) x) x)) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
3 calls:
| 5.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | x |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | eps |
| 98.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal 2/3 binary64)) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 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)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (*.f64 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 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))) eps) (pow (tan x) 2)) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
3 calls:
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
| 98.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (- (/ (+ (- 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))) eps) (pow (tan x) 2)) (*.f64 eps (*.f64 eps #s(literal 1/3 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) eps)) |
3 calls:
| 7.0ms | x |
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
| 98.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | x |
| 1.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 6.3% | 1 | x |
| 6.3% | 1 | eps |
| 6.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
3 calls:
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.3% | 1 | x |
| 5.3% | 1 | eps |
| 5.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 44× | *-commutative_binary64 |
| 12× | +-commutative_binary64 |
| 8× | sub-neg_binary64 |
| 6× | neg-sub0_binary64 |
| 6× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 148 | 650 |
| 1 | 181 | 650 |
| 2 | 192 | 650 |
| 3 | 198 | 650 |
| 4 | 202 | 650 |
| 5 | 203 | 650 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (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)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
| Outputs |
|---|
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) |
(*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(*.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (- (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)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 #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)) eps #s(approx (pow (tan x) 2) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 eps x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) eps) (pow (tan x) 2)) #s(approx (+ (* x (+ (* x (+ (* eps (* eps 4/3)) 1)) eps)) (* eps (* eps 1/3))) (*.f64 x (+.f64 x eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) (fma.f64 x (*.f64 x eps) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) #s(approx (+ (* x (* x eps)) eps) (*.f64 eps (*.f64 x x))))) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ x eps))) #s(literal 0 binary64)) |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 10 656× | lower-fma.f64 |
| 10 656× | lower-fma.f32 |
| 9 598× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 544 | 9119 |
| 1 | 1711 | 8503 |
| 2 | 5157 | 8205 |
| 0 | 8864 | 7855 |
| 0 | 83 | 704 |
| 0 | 127 | 692 |
| 0 | 622 | 659 |
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 0 | 459 | 7572 |
| 1 | 1345 | 7214 |
| 2 | 4084 | 6646 |
| 0 | 8100 | 6351 |
| 0 | 64 | 385 |
| 0 | 113 | 370 |
| 1 | 479 | 311 |
| 2 | 3862 | 311 |
| 0 | 8184 | 307 |
| 0 | 590 | 14038 |
| 1 | 1880 | 13738 |
| 2 | 6055 | 13318 |
| 0 | 8171 | 12679 |
| 0 | 52 | 368 |
| 0 | 97 | 339 |
| 1 | 432 | 241 |
| 2 | 3951 | 237 |
| 0 | 8143 | 229 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | 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× | iter limit |
| 1× | node limit |
Compiled 757 to 327 computations (56.8% saved)
Compiled 576 to 196 computations (66% saved)
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