
Time bar (total: 12.5s)
| 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)
| 4.0s | 25 712× | 0 | invalid |
| 1.1s | 5 041× | 1 | valid |
| 385.0ms | 3 215× | 0 | valid |
ival-sin: 913.0ms (25.2% of total)const: 611.0ms (16.8% of total)ival-sub: 391.0ms (10.8% of total)ival-fabs: 327.0ms (9% of total)ival-add: 284.0ms (7.8% of total)ival-mult: 277.0ms (7.6% of total)adjust: 235.0ms (6.5% of total)ival-<=: 224.0ms (6.2% of total)ival-<: 211.0ms (5.8% of total)ival-and: 102.0ms (2.8% of total)exact: 41.0ms (1.1% of total)ival-assert: 11.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 220 | 3 | (-5.526139394320619e-17 4.1519194956551108e-19) | 3 | (1.9851810955919863e-185 2.0315311783046448e-187) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) | cancellation | 220 | 6 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 2 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 219 | 2 |
| - | 3 | 32 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 219 | 2 | 0 |
| - | 3 | 4 | 28 |
| number | freq |
|---|---|
| 0 | 34 |
| 1 | 222 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 35.0ms | 300× | 1 | valid |
| 13.0ms | 212× | 0 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-sin: 13.0ms (40.4% of total)adjust: 9.0ms (28% of total)ival-sub: 5.0ms (15.5% of total)ival-add: 4.0ms (12.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 43 |
| 1 | 22 | 43 |
| 2 | 29 | 43 |
| 3 | 37 | 43 |
| 4 | 49 | 43 |
| 5 | 71 | 43 |
| 6 | 93 | 43 |
| 7 | 147 | 43 |
| 8 | 231 | 43 |
| 9 | 385 | 43 |
| 10 | 1010 | 43 |
| 11 | 4371 | 43 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 11 | 7 |
| 0 | 11 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.3% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 11 | 18 |
| 0 | 11 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(sin.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (+.f64 x eps) | |
| accuracy | 0.0 | (sin.f64 x) | |
| accuracy | 0.1114878714029668 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 23.361207239431575 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 16.0ms | 150× | 1 | valid |
| 5.0ms | 106× | 0 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sin: 5.0ms (37.6% of total)adjust: 4.0ms (30% of total)ival-add: 2.0ms (15% of total)ival-sub: 2.0ms (15% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps 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 (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 0.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 303 |
| 1 | 366 | 303 |
| 2 | 1224 | 296 |
| 3 | 4149 | 296 |
| 4 | 7986 | 296 |
| 0 | 8046 | 267 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps 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 (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
| Outputs |
|---|
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64))) x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(sin x) |
(sin.f64 x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x)) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 51 | 16 |
| 2 | 365 | 16 |
| 3 | 4452 | 16 |
| 0 | 8177 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(*.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (+.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) |
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(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(neg.f64 (/.f64 (*.f64 (neg.f64 (+.f64 eps x)) (-.f64 x eps)) (-.f64 x eps))) |
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))) |
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (*.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 eps (/.f64 (*.f64 eps eps) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))) |
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(+.f64 eps x) |
(+.f64 x eps) |
(sin.f64 x) |
Compiled 5 510 to 734 computations (86.7% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 169 | 8 | 177 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 169 | 9 | 178 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.5% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
| ▶ | 35.3% | (/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
| 36.4% | (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))))))) | |
| 63.5% | (-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) | |
| ✓ | 63.3% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| ▶ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| ▶ | 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 581 to 198 computations (65.9% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 7 | (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) | |
| cost-diff | 8 | (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) | |
| cost-diff | 15 | (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) | |
| cost-diff | 27 | (/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) | |
| cost-diff | 0 | (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) | |
| cost-diff | 0 | (cos.f64 eps) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) | |
| cost-diff | 0 | (*.f64 (sin.f64 x) eps) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| cost-diff | 0 | (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 2 | (+.f64 #s(literal 0 binary64) eps) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 430 |
| 0 | 75 | 388 |
| 1 | 148 | 388 |
| 2 | 401 | 354 |
| 3 | 1495 | 308 |
| 4 | 6424 | 308 |
| 0 | 8103 | 308 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(sin.f64 x) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(sin.f64 x) |
x |
(cos.f64 eps) |
eps |
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) |
(*.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
#s(literal 2 binary64) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(sin.f64 x) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(/.f64 eps #s(literal 2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(sin.f64 x) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(sin.f64 x) |
x |
(cos.f64 eps) |
eps |
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) |
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) |
(*.f64 (sin.f64 eps) (cos.f64 x)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(sin.f64 eps) |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(/.f64 (+.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) |
(pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
eps |
x |
#s(literal 2 binary64) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 x) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 11.436489652402313 | (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) | |
| accuracy | 26.090302292317613 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) | |
| accuracy | 26.11667789100429 | (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) | |
| accuracy | 27.02548026763016 | (/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) | |
| accuracy | 0.0 | (cos.f64 eps) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 eps) (cos.f64 x)) | |
| accuracy | 0.01953125 | (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) | |
| accuracy | 23.364584088803664 | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) | |
| accuracy | 0.006191259768442017 | (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) | |
| accuracy | 0.0078125 | (*.f64 (sin.f64 x) eps) | |
| accuracy | 0.015625 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 1.5909302673869277 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| accuracy | 0.0 | (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) | |
| accuracy | 0.0 | (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) | |
| accuracy | 0.0234375 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.05214346935246515 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| 101.0ms | 165× | 1 | valid |
| 23.0ms | 88× | 0 | valid |
| 7.0ms | 3× | 3 | valid |
Compiled 425 to 44 computations (89.6% saved)
adjust: 24.0ms (23.4% of total)ival-mult: 20.0ms (19.5% of total)ival-sin: 16.0ms (15.6% of total)ival-add: 12.0ms (11.7% of total)ival-div: 10.0ms (9.7% of total)ival-cos: 8.0ms (7.8% of total)ival-pow2: 7.0ms (6.8% of total)ival-sub: 5.0ms (4.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(sin.f64 x) |
(cos.f64 eps) |
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(*.f64 (sin.f64 eps) (cos.f64 x)) |
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
| Outputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(+ (sin eps) (* -1 x)) |
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1))) |
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (+ (* x (- (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (* 2 (/ (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps)))) (sin eps))) (+ (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (pow (sin eps) 2))) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ 1/6 (+ (* -1 (cos eps)) (+ (* -1 (+ 1 (cos eps))) (+ (* -1/3 (cos eps)) (+ (* 2 (- (* -1/6 (cos eps)) 1/6)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (pow (sin eps) 2))) (+ (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 3)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps))))))))) (sin eps)) (/ (* (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))) (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))))))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(pow (sin eps) 2) |
(+ (* x (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (+ (* 4 (pow (cos eps) 2)) (* x (- (+ (* 2 (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (sin eps)))) (+ (* -1 (* (sin eps) (+ 1 (cos eps)))) (+ (* 2 (* (sin eps) (- (* -1/6 (cos eps)) 1/6))) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (sin eps))) (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))))))))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps)))))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps))))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(/ (pow x 2) (sin eps)) |
(* (pow x 2) (+ (* -1 (* x (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* (pow x 2) (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* (pow x 2) (+ (* x (- (* x (- (+ (* 1/2 (/ 1 (sin eps))) (* x (- (* 1/6 (/ 1 (pow (sin eps) 2))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (sin eps))))))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(sin x) |
(- (* (cos x) (sin eps)) (sin x)) |
(/ (- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))))) |
(- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) |
(/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* (cos x) (sin eps)) |
(/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x))))))) |
(- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x)))))) |
(/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x))))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* 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)))) |
(cos x) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(* -1 (sin x)) |
(- (* eps (cos x)) (sin x)) |
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x)) |
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x)) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 3))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 3)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 3))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x))))))))) (sin x)) (+ (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))) (sin x)) (/ (* (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x)))))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (* (cos x) (sin x))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2)))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (sin x))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 2)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (sin x))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(+ (sin x) (* eps (- (cos x) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x))))) |
(* 1/4 (pow (sin x) 2)) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x)))))) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x)))))) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x)))))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x)))))))) |
(* 1/2 (sin x)) |
(+ (* 1/2 (sin x)) (* eps (- (cos x) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/24 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x))))) |
(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x))) |
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(cos eps) |
(sin (* 1/2 eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))) |
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 38.0ms | x | @ | -inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) |
| 16.0ms | eps | @ | 0 | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) |
| 14.0ms | eps | @ | inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) |
| 11.0ms | x | @ | 0 | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) |
| 9.0ms | x | @ | inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 931 | 7410 |
| 1 | 3271 | 6906 |
| 0 | 8239 | 6495 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(+ (sin eps) (* -1 x)) |
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1))) |
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (+ (* x (- (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (* 2 (/ (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps)))) (sin eps))) (+ (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (pow (sin eps) 2))) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ 1/6 (+ (* -1 (cos eps)) (+ (* -1 (+ 1 (cos eps))) (+ (* -1/3 (cos eps)) (+ (* 2 (- (* -1/6 (cos eps)) 1/6)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (pow (sin eps) 2))) (+ (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 3)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps))))))))) (sin eps)) (/ (* (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))) (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))))))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))))) |
(pow (sin eps) 2) |
(+ (* x (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (+ (* 4 (pow (cos eps) 2)) (* x (- (+ (* 2 (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (sin eps)))) (+ (* -1 (* (sin eps) (+ 1 (cos eps)))) (+ (* 2 (* (sin eps) (- (* -1/6 (cos eps)) 1/6))) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (sin eps))) (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))))))))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2)) |
(+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps)))))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps))))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps))))) |
(/ (pow x 2) (sin eps)) |
(* (pow x 2) (+ (* -1 (* x (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* (pow x 2) (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* (pow x 2) (+ (* x (- (* x (- (+ (* 1/2 (/ 1 (sin eps))) (* x (- (* 1/6 (/ 1 (pow (sin eps) 2))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (sin eps))))))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(sin x) |
(- (* (cos x) (sin eps)) (sin x)) |
(/ (- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))))) |
(- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) |
(/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* (cos x) (sin eps)) |
(/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(/ (- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x))))))) |
(- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x)))))) |
(/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x))))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* 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)))) |
(cos x) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(* -1 (sin x)) |
(- (* eps (cos x)) (sin x)) |
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x)) |
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x)) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 3))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 3)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 3))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x))))))))) (sin x)) (+ (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))) (sin x)) (/ (* (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x)))))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
(* eps (* (cos x) (sin x))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2)))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (sin x))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 2)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (sin x))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x)))) |
(+ (sin x) (* eps (- (cos x) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x))))) |
(* 1/4 (pow (sin x) 2)) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x)))))) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x)))))) |
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x)))))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x)))))))) |
(* 1/2 (sin x)) |
(+ (* 1/2 (sin x)) (* eps (- (cos x) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/24 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x))))) |
(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x))) |
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(cos eps) |
(sin (* 1/2 eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))) |
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
| Outputs |
|---|
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
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(sin eps) |
(sin.f64 eps) |
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eps |
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1 |
#s(literal 1 binary64) |
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(* eps x) |
(*.f64 x eps) |
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x |
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(pow (sin eps) 2) |
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(* (cos x) (sin eps)) |
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(* eps (cos x)) |
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(cos x) |
(cos.f64 x) |
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(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
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(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))))) |
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(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos 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(* eps (* (cos x) (sin x))) |
(*.f64 (*.f64 (cos.f64 x) eps) (sin.f64 x)) |
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(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x))) |
(fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) |
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(fma.f64 (fma.f64 (neg.f64 eps) (*.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) |
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x))))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) (cos.f64 x)) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/48 binary64)))) eps (*.f64 #s(literal 1/8 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x))))) eps (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(cos eps) |
(cos.f64 eps) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps)))) |
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))) |
(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))) (/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))) |
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) |
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 348 |
| 0 | 75 | 213 |
| 1 | 334 | 203 |
| 2 | 3024 | 203 |
| 0 | 8458 | 203 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(sin.f64 x) |
(cos.f64 eps) |
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(*.f64 (sin.f64 eps) (cos.f64 x)) |
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
| Outputs |
|---|
(pow.f64 eps #s(literal 1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps))) |
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps))) |
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps)) |
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))) |
(/.f64 (*.f64 eps eps) eps) |
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps)) |
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps) |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
(/.f64 (-.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64)) |
(/.f64 (fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64)) |
(/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64))) |
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64)) |
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)) |
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64))) |
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64))) |
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64))) |
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(+.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
(sin.f64 eps) |
(-.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (sin.f64 eps)))) |
(+.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps))) |
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) (*.f64 eps eps)) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))) |
(/.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (neg.f64 eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (*.f64 eps eps))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (neg.f64 eps))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (*.f64 eps eps))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (neg.f64 eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))) |
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(*.f64 (pow.f64 (/.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))) #s(literal 1 binary64))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 (+.f64 x eps)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))) |
(*.f64 (sin.f64 x) (fabs.f64 (/.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(*.f64 (sin.f64 x) (sqrt.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(*.f64 (sin.f64 x) (sqrt.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))) |
(*.f64 (sin.f64 x) (pow.f64 (/.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1 binary64))) |
(*.f64 (sin.f64 x) (/.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(pow.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1 binary64)) |
(/.f64 (fabs.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (fabs.f64 (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (sqrt.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))) |
(/.f64 (sqrt.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) (sqrt.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fabs.f64 (fabs.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fabs.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64))) |
(fabs.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(fabs.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(exp.f64 (/.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal 1 binary64))) |
Compiled 78 434 to 4 100 computations (94.8% saved)
18 alts after pruning (16 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 064 | 14 | 1 078 |
| Fresh | 1 | 2 | 3 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 069 | 18 | 1 087 |
| Status | Accuracy | Program |
|---|---|---|
| 63.5% | (-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) | |
| ✓ | 63.3% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
| 99.0% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| ▶ | 99.7% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.6% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.4% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ▶ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| 98.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) | |
| ▶ | 98.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
| 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) | |
| ▶ | 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
| 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) | |
| 98.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) | |
| 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
Compiled 795 to 565 computations (28.9% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 1 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 1 | (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) | |
| cost-diff | 2 | (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | #s(approx (* (sin x) eps) (*.f64 x eps)) | |
| cost-diff | 0 | (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) | |
| cost-diff | 1 | (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) | |
| cost-diff | 2 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 4 | (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 434 |
| 0 | 95 | 423 |
| 1 | 169 | 414 |
| 2 | 485 | 414 |
| 3 | 1931 | 404 |
| 4 | 4977 | 404 |
| 5 | 7693 | 404 |
| 0 | 8002 | 386 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)) |
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) |
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
(PI.f64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) |
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) |
#s(literal -1/2 binary64) |
(+.f64 x eps) |
x |
eps |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) |
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) |
#s(literal -1/322560 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/1920 binary64) |
#s(literal 1/24 binary64) |
#s(literal 1 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
#s(literal 2 binary64) |
x |
#s(literal -2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)) |
(/.f64 (-.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64)) |
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) |
(-.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps)) |
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
(PI.f64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(+.f64 x eps) |
x |
eps |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) |
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) |
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) |
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) |
#s(literal -1/322560 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/1920 binary64) |
#s(literal 1/24 binary64) |
#s(literal 1 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
x |
#s(literal -2 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0234375 | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.05214346935246515 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.15625 | (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) | |
| accuracy | 0.17842381862999004 | #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.006191259768442017 | (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) | |
| accuracy | 0.015625 | (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| accuracy | 1.595309492160216 | #s(approx (* (sin x) eps) (*.f64 x eps)) | |
| accuracy | 0.0 | (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) | |
| accuracy | 0.015625 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) | |
| accuracy | 1.2916828726678498 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) | |
| accuracy | 0.015625 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) | |
| accuracy | 1.602091357030652 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) | |
| accuracy | 0.0 | (PI.f64) | |
| accuracy | 0.0234375 | (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) | |
| accuracy | 0.0234375 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) | |
| accuracy | 0.05978930347432946 | (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
| 133.0ms | 149× | 1 | valid |
| 41.0ms | 107× | 0 | valid |
Compiled 332 to 50 computations (84.9% saved)
ival-sin: 35.0ms (24.4% of total)adjust: 32.0ms (22.3% of total)ival-mult: 32.0ms (22.3% of total)ival-add: 14.0ms (9.7% of total)const: 14.0ms (9.7% of total)ival-div: 6.0ms (4.2% of total)ival-cos: 4.0ms (2.8% of total)ival-sub: 3.0ms (2.1% of total)ival-pi: 2.0ms (1.4% of total)exact: 1.0ms (0.7% of total)ival-neg: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(sin (* 1/2 (- (PI) eps))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(- (PI) eps) |
(- (+ (PI) (* -2 x)) eps) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin (* 1/2 (- (PI) (+ eps (* 2 x))))) |
(* -2 x) |
(* x (- (/ (PI) x) (+ 2 (/ eps x)))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* eps (sin x)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* -1/2 x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps))) |
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (PI) (* 2 x)))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x))))))))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))))) |
(- (PI) (* 2 x)) |
(- (+ (PI) (* -1 eps)) (* 2 x)) |
(* eps (sin (* 1/2 (- (PI) (* 2 x))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(cos x) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
-1/24 |
(- (* 1/1920 (pow eps 2)) 1/24) |
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/1920 (pow eps 2)) |
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* -1 eps) |
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/322560 (pow eps 7)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* -1/322560 (pow eps 4)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))) |
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 24.0ms | x | @ | 0 | ((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2)))) |
| 5.0ms | x | @ | -inf | ((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2)))) |
| 4.0ms | eps | @ | -inf | ((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2)))) |
| 4.0ms | eps | @ | inf | ((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2)))) |
| 4.0ms | eps | @ | 0 | ((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 443 | 1757 |
| 1 | 1590 | 1707 |
| 2 | 5804 | 1692 |
| 0 | 8073 | 1564 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin (* 1/2 (- (PI) eps))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(- (PI) eps) |
(- (+ (PI) (* -2 x)) eps) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin (* 1/2 (- (PI) (+ eps (* 2 x))))) |
(* -2 x) |
(* x (- (/ (PI) x) (+ 2 (/ eps x)))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* eps (sin x)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* -1/2 x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps))) |
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (PI) (* 2 x)))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x))))))))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))))) |
(- (PI) (* 2 x)) |
(- (+ (PI) (* -1 eps)) (* 2 x)) |
(* eps (sin (* 1/2 (- (PI) (* 2 x))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(cos x) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
-1/24 |
(- (* 1/1920 (pow eps 2)) 1/24) |
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/1920 (pow eps 2)) |
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* -1 eps) |
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/322560 (pow eps 7)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* -1/322560 (pow eps 4)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))) |
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
| Outputs |
|---|
(sin (* 1/2 (- (PI) eps))) |
(sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(fma.f64 (neg.f64 x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(- (PI) eps) |
(-.f64 (PI.f64) eps) |
(- (+ (PI) (* -2 x)) eps) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(*.f64 #s(literal -2 binary64) (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) x (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x)) x (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(* eps x) |
(*.f64 eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) x) x (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 eps x)) |
(cos (* -1/2 eps)) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(+ (* -1/2 eps) (* -1/2 x)) |
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 (neg.f64 x) x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 x x))) |
(sin (* 1/2 (- (PI) (+ eps (* 2 x))))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(* -2 x) |
(*.f64 #s(literal -2 binary64) x) |
(* x (- (/ (PI) x) (+ 2 (/ eps x)))) |
(*.f64 (-.f64 (/.f64 (-.f64 (PI.f64) eps) x) #s(literal 2 binary64)) x) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(*.f64 (*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)) |
(* eps (sin x)) |
(*.f64 (sin.f64 x) eps) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) |
(* -1/2 x) |
(*.f64 #s(literal -1/2 binary64) x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x))))) |
(*.f64 (neg.f64 x) (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (PI.f64) eps) x))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(*.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (- (PI) (* 2 x)))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))) |
(fma.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (*.f64 #s(literal -1/8 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))))) eps (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) |
(- (PI) (* 2 x)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
(- (+ (PI) (* -1 eps)) (* 2 x)) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(* eps (sin (* 1/2 (- (PI) (* 2 x))))) |
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/6 binary64)) eps (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/6 binary64))) eps (*.f64 (cos.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(cos x) |
(cos.f64 x) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/1920 binary64) eps) eps (-.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) #s(literal 1/24 binary64))) eps) |
-1/24 |
#s(literal -1/24 binary64) |
(- (* 1/1920 (pow eps 2)) 1/24) |
(-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24) |
(fma.f64 (*.f64 #s(literal 1/1920 binary64) eps) eps (-.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) #s(literal 1/24 binary64))) |
(cos (* -1 x)) |
(cos.f64 x) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* 1/1920 (pow eps 2)) |
(*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) |
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) |
(* eps (cos (* -1 x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* -1 eps) |
(neg.f64 eps) |
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps))))) |
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64)) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* -1/2 (* eps x)) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(* -1/322560 (pow eps 7)) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/322560 binary64)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(*.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (pow.f64 eps #s(literal 7 binary64))) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 7 binary64))) |
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -1/1920 binary64) (*.f64 eps eps))) (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64))) (pow.f64 eps #s(literal 7 binary64))) |
(* -1/322560 (pow eps 4)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64))) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps))))) |
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/322560 binary64) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(*.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 7 binary64))) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 338 |
| 0 | 95 | 324 |
| 1 | 348 | 324 |
| 2 | 2717 | 324 |
| 0 | 8325 | 318 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(PI.f64) |
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(neg.f64 (sin.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (+.f64 (neg.f64 eps) (PI.f64))) #s(literal -2 binary64)))) |
(fma.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))) |
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))) |
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (neg.f64 (*.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 (neg.f64 eps)))) |
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps))) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 (-.f64 eps #s(literal 0 binary64)))) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 eps)) |
(pow.f64 (neg.f64 eps) #s(literal 1 binary64)) |
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) |
(pow.f64 eps #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 eps)) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps)))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps)))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))) |
(/.f64 (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 eps eps)) |
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eps |
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(*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64)))) |
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64)))) |
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) |
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))) |
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) |
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))) |
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (PI.f64))) |
(pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64)) |
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64)) |
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) |
(pow.f64 (PI.f64) #s(literal 1 binary64)) |
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) |
(sqrt.f64 (*.f64 (PI.f64) (PI.f64))) |
(fabs.f64 (neg.f64 (PI.f64))) |
(fabs.f64 (PI.f64)) |
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64)))) |
(exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) #s(literal 2 binary64))) |
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64))) |
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64))) |
(exp.f64 (log.f64 (PI.f64))) |
(log.f64 (exp.f64 (PI.f64))) |
(PI.f64) |
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) #s(literal -1/2 binary64)) (-.f64 x eps)) |
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps)) |
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps))) |
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps))))) |
(fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal -1/2 binary64) x)) |
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/2 binary64) eps)) |
(fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) |
(fma.f64 x #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (neg.f64 eps) #s(literal -1/2 binary64))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) |
(+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) x)) |
(+.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps)) |
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) |
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))) |
(*.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3686400 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) #s(literal 1/1920 binary64))) |
(/.f64 (*.f64 (fma.f64 #s(literal -1/33560740233216000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/7077888000 binary64)) (*.f64 eps eps)) (fma.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/3686400 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/619315200 binary64))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3686400 binary64))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) #s(literal 1/1920 binary64))) |
(/.f64 (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/33560740233216000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/7077888000 binary64))) (fma.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/3686400 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/619315200 binary64))))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps) (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps))) |
(fma.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/1920 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)))) |
(fma.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)) |
(fma.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(fma.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)) |
(+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps)) (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps))) |
(+.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64))) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
Compiled 19 074 to 2 647 computations (86.1% saved)
18 alts after pruning (13 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 508 | 9 | 517 |
| Fresh | 7 | 4 | 11 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 517 | 18 | 535 |
| Status | Accuracy | Program |
|---|---|---|
| 63.5% | (-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) | |
| ✓ | 63.3% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.0% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.7% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| ▶ | 99.4% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| ✓ | 98.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
| 97.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) | |
| 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) | |
| ▶ | 97.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
| 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) | |
| ▶ | 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
| ✓ | 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
| ▶ | 99.9% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
| ▶ | 98.7% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
Compiled 874 to 605 computations (30.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 1 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 2 | (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) | |
| cost-diff | 0 | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) | |
| cost-diff | 1 | (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) | |
| cost-diff | 2 | (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) | |
| cost-diff | 0 | #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) | |
| cost-diff | 0 | (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| cost-diff | 1 | (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 79 | 609 |
| 0 | 113 | 599 |
| 1 | 210 | 593 |
| 2 | 600 | 593 |
| 3 | 2304 | 576 |
| 4 | 6343 | 576 |
| 0 | 8110 | 535 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) |
#s(literal 2 binary64) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
#s(literal -2 binary64) |
x |
(-.f64 (PI.f64) eps) |
(PI.f64) |
eps |
#s(literal 1/2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 eps x) |
eps |
x |
#s(literal -1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(literal -1/2 binary64) |
x |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal 1 binary64) |
eps |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
#s(literal -2 binary64) |
x |
(PI.f64) |
#s(literal 1/2 binary64) |
eps |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) |
#s(literal -1/24 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
#s(literal 2 binary64) |
x |
#s(literal -2 binary64) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x)) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
#s(literal -2 binary64) |
x |
(-.f64 (PI.f64) eps) |
(PI.f64) |
eps |
#s(literal 1/2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64)) |
(*.f64 eps x) |
(*.f64 x eps) |
eps |
x |
#s(literal -1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(literal -1/2 binary64) |
x |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal 1 binary64) |
eps |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))) eps)) |
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))) eps) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
#s(literal -2 binary64) |
x |
(PI.f64) |
#s(literal 1/2 binary64) |
eps |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps)) |
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps) |
(fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) |
#s(literal -1/24 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
x |
#s(literal -2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0234375 | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.05214346935246515 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.17842381862999004 | #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.569230699257536 | #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) | |
| accuracy | 0.0078125 | (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) | |
| accuracy | 0.015625 | (fma.f64 #s(literal -2 binary64) x (PI.f64)) | |
| accuracy | 0.04502920705492342 | (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) | |
| accuracy | 0.8026261453645851 | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) | |
| accuracy | 0.015625 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) | |
| accuracy | 0.1875 | (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) | |
| accuracy | 1.2916828726678498 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) | |
| accuracy | 0.0234375 | (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) | |
| accuracy | 0.6346448248216612 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) | |
| accuracy | 1.2916828726678498 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) | |
| accuracy | 61.781129481028145 | #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) | |
| accuracy | 0.01171875 | (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) | |
| accuracy | 0.01171875 | (-.f64 (PI.f64) eps) | |
| accuracy | 0.0234375 | (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.05978930347432946 | (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
| 234.0ms | 149× | 1 | valid |
| 92.0ms | 107× | 0 | valid |
Compiled 389 to 73 computations (81.2% saved)
ival-sin: 105.0ms (40.9% of total)ival-mult: 57.0ms (22.2% of total)adjust: 35.0ms (13.6% of total)ival-add: 20.0ms (7.8% of total)const: 14.0ms (5.5% of total)ival-div: 11.0ms (4.3% of total)ival-sub: 5.0ms (1.9% of total)ival-cos: 4.0ms (1.6% of total)ival-pi: 2.0ms (0.8% of total)exact: 1.0ms (0.4% of total)ival-neg: 1.0ms (0.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(-.f64 (PI.f64) eps) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
(* 1/2 (- (PI) eps)) |
(+ (* -1 x) (* 1/2 (- (PI) eps))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(* 2 (sin (* 1/2 (- (PI) eps)))) |
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps))))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* 1/2 (PI)) |
(+ (* -1 x) (* 1/2 (PI))) |
(* eps (sin (* 1/2 (PI)))) |
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI))))) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI))))))))) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI))))))))))) |
(sin (* 1/2 (PI))) |
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI)))))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI)))))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin (* 1/2 (- (PI) eps))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(- (PI) eps) |
(- (+ (PI) (* -2 x)) eps) |
(* -1/2 (* eps x)) |
(PI) |
(+ (PI) (* -2 x)) |
(* -1 x) |
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1)) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))) |
(* 2 (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* x (- (* 1/2 (/ (PI) x)) 1)) |
(* eps (sin (* 1/2 (- (PI) (* 2 x))))) |
(sin (* 1/2 (- (PI) (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (PI) (+ eps (* 2 x))))) |
(* -2 x) |
(* x (- (/ (PI) x) (+ 2 (/ eps x)))) |
(* x (- (/ (PI) x) 2)) |
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))) |
(* 2 (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x))))) |
(* eps (sin (* 1/2 (+ (PI) (* -2 x))))) |
(sin (* 1/2 (+ (PI) (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps))) |
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x))))) |
(* -1 (* x (+ 2 (* -1 (/ (PI) x))))) |
(* 1/2 (+ (PI) (* -2 x))) |
(+ (* -1/2 eps) (* 1/2 (+ (PI) (* -2 x)))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x))))))))))))) |
(* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) |
(+ (* -1 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (sin (* 1/2 (+ (PI) (* -2 x)))))) |
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/4 (* eps (sin (* 1/2 (+ (PI) (* -2 x))))))))) |
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/4 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(cos x) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x))))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))))) |
(+ (PI) (* -1 eps)) |
(+ (PI) (+ (* -2 x) (* -1 eps))) |
-1/24 |
(- (* 1/1920 (pow eps 2)) 1/24) |
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24) |
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/322560 (pow eps 7)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* -1 eps) |
(* eps (- (/ (PI) eps) 1)) |
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1)) |
(* -1/322560 (pow eps 4)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* 2 (sin (* 1/2 eps))) |
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))) |
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 21.0ms | eps | @ | -inf | ((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2)) |
| 6.0ms | eps | @ | 0 | ((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2)) |
| 5.0ms | eps | @ | inf | ((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2)) |
| 4.0ms | x | @ | inf | ((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2)) |
| 4.0ms | x | @ | -inf | ((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 550 | 2318 |
| 1 | 2042 | 2143 |
| 2 | 7137 | 2129 |
| 0 | 8342 | 1993 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 (- (PI) eps)) |
(+ (* -1 x) (* 1/2 (- (PI) eps))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(* 2 (sin (* 1/2 (- (PI) eps)))) |
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps))))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* 1/2 (PI)) |
(+ (* -1 x) (* 1/2 (PI))) |
(* eps (sin (* 1/2 (PI)))) |
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI))))) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI))))))))) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI))))))))))) |
(sin (* 1/2 (PI))) |
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI)))))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI)))))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin (* 1/2 (- (PI) eps))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(- (PI) eps) |
(- (+ (PI) (* -2 x)) eps) |
(* -1/2 (* eps x)) |
(PI) |
(+ (PI) (* -2 x)) |
(* -1 x) |
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1)) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))) |
(* 2 (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* x (- (* 1/2 (/ (PI) x)) 1)) |
(* eps (sin (* 1/2 (- (PI) (* 2 x))))) |
(sin (* 1/2 (- (PI) (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (PI) (+ eps (* 2 x))))) |
(* -2 x) |
(* x (- (/ (PI) x) (+ 2 (/ eps x)))) |
(* x (- (/ (PI) x) 2)) |
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))) |
(* 2 (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x))))) |
(* eps (sin (* 1/2 (+ (PI) (* -2 x))))) |
(sin (* 1/2 (+ (PI) (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps))) |
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x))))) |
(* -1 (* x (+ 2 (* -1 (/ (PI) x))))) |
(* 1/2 (+ (PI) (* -2 x))) |
(+ (* -1/2 eps) (* 1/2 (+ (PI) (* -2 x)))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x)))))))))))) |
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x))))))))))))) |
(* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) |
(+ (* -1 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (sin (* 1/2 (+ (PI) (* -2 x)))))) |
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/4 (* eps (sin (* 1/2 (+ (PI) (* -2 x))))))))) |
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/4 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(cos x) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x))))))))) |
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))))) |
(+ (PI) (* -1 eps)) |
(+ (PI) (+ (* -2 x) (* -1 eps))) |
-1/24 |
(- (* 1/1920 (pow eps 2)) 1/24) |
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24) |
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/322560 (pow eps 7)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* -1 eps) |
(* eps (- (/ (PI) eps) 1)) |
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1)) |
(* -1/322560 (pow eps 4)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560)) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(* 2 (sin (* 1/2 eps))) |
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))) |
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps))))) |
| Outputs |
|---|
(* 1/2 (- (PI) eps)) |
(*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) |
(+ (* -1 x) (* 1/2 (- (PI) eps))) |
(-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))) |
(*.f64 #s(literal -2 binary64) (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) x (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) |
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x)) x (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) |
(* 2 (sin (* 1/2 (- (PI) eps)))) |
(*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps))))) |
(*.f64 #s(literal -2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(fma.f64 (fma.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) x (*.f64 (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) #s(literal -2 binary64))) x (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))) x (*.f64 (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) #s(literal -2 binary64))) x (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 eps x) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(* 1/2 (PI)) |
(*.f64 #s(literal 1/2 binary64) (PI.f64)) |
(+ (* -1 x) (* 1/2 (PI))) |
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x) |
(* eps (sin (* 1/2 (PI)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps) |
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI))))) |
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI))))))))) |
(fma.f64 (fma.f64 (neg.f64 eps) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)) |
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI))))))))))) |
(fma.f64 (fma.f64 (neg.f64 eps) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) eps))) x)) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)) |
(sin (* 1/2 (PI))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) |
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI)))))) |
(fma.f64 (neg.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))))) |
(fma.f64 (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(cos (* -1/2 eps)) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 x (neg.f64 x)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(sin (* 1/2 (- (PI) eps))) |
(sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) |
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps)))))) |
(fma.f64 (neg.f64 x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps)))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) |
(- (PI) eps) |
(-.f64 (PI.f64) eps) |
(- (+ (PI) (* -2 x)) eps) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(* -1/2 (* eps x)) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(PI) |
(PI.f64) |
(+ (PI) (* -2 x)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1)) |
(*.f64 (-.f64 (*.f64 (/.f64 (-.f64 (PI.f64) eps) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) |
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(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64))) |
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 4 binary64))) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps))))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x) eps) #s(literal 1/2 binary64))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x)))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))) |
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))) |
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))) |
(*.f64 (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps)))) |
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2)))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/322560 binary64) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2)))))) |
(*.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64))) |
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6)))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 7 binary64))) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))) |
(sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)) |
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps))))) |
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (PI.f64) eps))) |
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps))))) |
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 79 | 497 |
| 0 | 113 | 481 |
| 1 | 432 | 481 |
| 2 | 3543 | 481 |
| 0 | 8398 | 464 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))) |
(-.f64 (PI.f64) eps) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))) |
(*.f64 (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)) |
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)))) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))) |
(fma.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64) (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps))) |
(fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64)))) |
(fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) |
(/.f64 (-.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) (-.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 3 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))))) |
(+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) |
(*.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (*.f64 eps eps)) |
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))))) |
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
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(/.f64 (-.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (+.f64 eps (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) |
(-.f64 (-.f64 (PI.f64) #s(literal 0 binary64)) eps) |
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) (+.f64 eps (PI.f64))) (/.f64 (*.f64 eps eps) (+.f64 eps (PI.f64)))) |
(-.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 eps (+.f64 eps (PI.f64)) (*.f64 (PI.f64) (PI.f64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (+.f64 eps (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) |
(-.f64 (-.f64 (PI.f64) eps) #s(literal 0 binary64)) |
(-.f64 (PI.f64) eps) |
(/.f64 (-.f64 (pow.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) #s(literal 2 binary64)) (*.f64 eps eps)) (+.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) eps)) |
(/.f64 (-.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))) |
(/.f64 (-.f64 (pow.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) #s(literal 2 binary64)) (fma.f64 eps eps (*.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) eps)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64))))))) |
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64))) (neg.f64 eps)) (*.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) (neg.f64 (*.f64 eps eps)))) (*.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) (neg.f64 eps))) |
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64))) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) (*.f64 eps eps))) |
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (neg.f64 eps)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))) (neg.f64 (*.f64 eps eps)))) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))) (neg.f64 eps))) |
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (*.f64 eps eps)) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))) (*.f64 eps eps))) |
(/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64))) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 (PI.f64) eps))))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))) |
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (-.f64 (PI.f64) eps)) |
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (-.f64 (PI.f64) eps)) |
(fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) |
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) |
(-.f64 (-.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) #s(literal 0 binary64)) eps) |
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)) (/.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps))) |
(-.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) eps) |
(-.f64 (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) #s(literal 0 binary64)) |
(-.f64 (-.f64 (PI.f64) eps) (*.f64 (neg.f64 x) #s(literal -2 binary64))) |
(-.f64 (-.f64 (PI.f64) eps) (*.f64 #s(literal 2 binary64) x)) |
(-.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps)) |
(+.f64 (/.f64 (pow.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))) (/.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64))))))) |
(+.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 (PI.f64) eps)) |
(+.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64))) |
(+.f64 (PI.f64) (-.f64 (*.f64 x #s(literal -2 binary64)) eps)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) eps) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps x)) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) x)) |
(*.f64 x (*.f64 #s(literal -1/2 binary64) eps)) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) x)) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal -1/2 binary64) x)) (*.f64 eps eps)) |
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64)))) (neg.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))))) |
(/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))))) |
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))) |
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (PI.f64)) |
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (PI.f64)) |
(fma.f64 x #s(literal -2 binary64) (PI.f64)) |
(fma.f64 #s(literal -2 binary64) x (PI.f64)) |
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)))) |
(-.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))) |
(-.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))) |
(-.f64 (PI.f64) (*.f64 (neg.f64 x) #s(literal -2 binary64))) |
(-.f64 (PI.f64) (*.f64 #s(literal 2 binary64) x)) |
(+.f64 (/.f64 (pow.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))))) (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))))) |
(+.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) |
(+.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))) |
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) |
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
Compiled 22 421 to 2 483 computations (88.9% saved)
21 alts after pruning (14 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 469 | 7 | 476 |
| Fresh | 1 | 7 | 8 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 5 | 5 |
| Total | 473 | 21 | 494 |
| Status | Accuracy | Program |
|---|---|---|
| 63.5% | (-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) | |
| ✓ | 63.3% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.7% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| 99.3% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) | |
| 99.3% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) | |
| 99.4% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| 98.7% | (*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) | |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) | |
| 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| ✓ | 98.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
| 97.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) | |
| 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) | |
| ✓ | 97.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
| 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) | |
| ✓ | 5.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
| ✓ | 97.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
| 99.9% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) | |
| 98.7% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
Compiled 1 907 to 708 computations (62.9% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))) |
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
3 calls:
| 56.0ms | x |
| 9.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) |
3 calls:
| 26.0ms | x |
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 8.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 12.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.0ms | x |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
3 calls:
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 15.0ms | x |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
3 calls:
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
3 calls:
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
3 calls:
| 20.0ms | eps |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 1 | eps |
| 98.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.0% | 1 | x |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
3 calls:
| 2.0ms | eps |
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
3 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.5% | 1 | x |
| 97.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
3 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.5% | 1 | x |
| 97.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Total -59.2b remaining (-3719.9%)
Threshold costs -59.2b (-3719.9%)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
3 calls:
| 1.0ms | eps |
| 1.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.5% | 1 | x |
| 97.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 113 | 345 |
| 1 | 178 | 343 |
| 2 | 412 | 342 |
| 3 | 1658 | 342 |
| 4 | 4745 | 340 |
| 5 | 6902 | 340 |
| 1× | node limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 931 | 7410 |
| 1 | 3271 | 6906 |
| 0 | 8239 | 6495 |
| 0 | 42 | 348 |
| 0 | 75 | 213 |
| 1 | 334 | 203 |
| 2 | 3024 | 203 |
| 0 | 8458 | 203 |
| 0 | 550 | 2318 |
| 1 | 2042 | 2143 |
| 2 | 7137 | 2129 |
| 0 | 8342 | 1993 |
| 0 | 107 | 303 |
| 1 | 366 | 303 |
| 2 | 1224 | 296 |
| 3 | 4149 | 296 |
| 4 | 7986 | 296 |
| 0 | 8046 | 267 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 51 | 16 |
| 2 | 365 | 16 |
| 3 | 4452 | 16 |
| 0 | 8177 | 16 |
| 0 | 443 | 1757 |
| 1 | 1590 | 1707 |
| 2 | 5804 | 1692 |
| 0 | 8073 | 1564 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 355 to 118 computations (66.8% saved)
Compiled 754 to 274 computations (63.7% saved)
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