
Time bar (total: 12.1s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.7s | 25 762× | 0 | invalid |
| 660.0ms | 2 732× | 1 | valid |
| 655.0ms | 5 524× | 0 | valid |
const: 874.0ms (25.7% of total)ival-sin: 734.0ms (21.6% of total)ival-<=: 322.0ms (9.5% of total)ival-<: 271.0ms (8% of total)ival-fabs: 259.0ms (7.6% of total)ival-mult: 246.0ms (7.2% of total)ival-add: 232.0ms (6.8% of total)ival-sub: 208.0ms (6.1% of total)ival-and: 110.0ms (3.2% of total)adjust: 84.0ms (2.5% of total)exact: 51.0ms (1.5% of total)ival-assert: 13.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 224 | 6 | (5.4130600052629094e-154 4.3236115264724973e-156) | 3 | (7.650697013324092e-171 1.1824122930459035e-172) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3 | 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 | 227 | 8 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 3 | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 222 | 4 |
| - | 6 | 24 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 222 | 4 | 0 |
| - | 6 | 5 | 19 |
| number | freq |
|---|---|
| 0 | 28 |
| 1 | 226 |
| 2 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 26.0ms | 190× | 1 | valid |
| 17.0ms | 320× | 0 | valid |
| 1.0ms | 2× | 2 | valid |
Compiled 83 to 34 computations (59% saved)
ival-sin: 13.0ms (55.5% of total)adjust: 4.0ms (17.1% of total)ival-add: 3.0ms (12.8% of total)ival-sub: 3.0ms (12.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (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 |
|---|---|---|
| ▶ | 60.6% | (-.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 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (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 | (+.f64 x eps) | |
| accuracy | 0 | (sin.f64 x) | |
| accuracy | 0.11659089903970274 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 25.067190041653237 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 10.0ms | 95× | 1 | valid |
| 8.0ms | 160× | 0 | valid |
| 0.0ms | 1× | 2 | valid |
Compiled 38 to 14 computations (63.2% saved)
ival-sin: 5.0ms (49.8% of total)adjust: 2.0ms (19.9% of total)ival-add: 2.0ms (19.9% of total)ival-sub: 2.0ms (19.9% 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 | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 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)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 291 |
| 1 | 314 | 291 |
| 2 | 779 | 284 |
| 3 | 2842 | 284 |
| 4 | 6177 | 284 |
| 0 | 8125 | 253 |
| 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)) (fma.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 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #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 eps x) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (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) #s(literal -1/6 binary64)) eps)) 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) #s(literal -1/2 binary64)) eps (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 eps x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 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 (pow.f64 (/.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 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.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 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (sin.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) #s(literal -1 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 (-.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 3 binary64)) (pow.f64 (sin.f64 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)))) |
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(neg.f64 (sin.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 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(sin.f64 (+.f64 eps x)) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (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 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (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 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x)) |
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 #s(literal 1 binary64) (+.f64 eps x)) |
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (*.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.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)))) |
(/.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 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.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 (*.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)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 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 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(+.f64 eps x) |
(+.f64 x eps) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 1 binary64)) |
(sin.f64 x) |
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64))) |
Compiled 6 283 to 852 computations (86.4% saved)
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 226 | 9 | 235 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 226 | 10 | 236 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 36.3% | (fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
| ▶ | 99.8% | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
| 99.8% | (fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) | |
| 36.1% | (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))) | |
| ✓ | 60.6% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.8% | (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) | |
| ▶ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| ▶ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 303 to 204 computations (32.7% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 eps x) | |
| cost-diff | 0 | (sin.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) | |
| cost-diff | 20288 | (fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) | |
| cost-diff | 0 | (cos.f64 x) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) | |
| cost-diff | 6400 | (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) | |
| cost-diff | 0 | (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (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 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) eps) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 211 |
| 0 | 69 | 201 |
| 1 | 113 | 189 |
| 2 | 223 | 187 |
| 3 | 406 | 187 |
| 4 | 650 | 187 |
| 5 | 1521 | 187 |
| 6 | 3052 | 187 |
| 7 | 4772 | 187 |
| 8 | 6307 | 187 |
| 9 | 6868 | 187 |
| 10 | 7306 | 187 |
| 11 | 7793 | 187 |
| 0 | 8100 | 187 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
#s(literal 1/2 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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
(sin.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) |
(cos.f64 eps) |
(sin.f64 x) |
(neg.f64 (sin.f64 x)) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(sin.f64 (-.f64 x eps)) |
(-.f64 x eps) |
(pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(neg.f64 (sin.f64 x)) |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #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 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)) |
(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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(sin.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) |
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) |
(cos.f64 eps) |
(sin.f64 x) |
(neg.f64 (sin.f64 x)) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) |
(*.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
eps |
x |
(sin.f64 (-.f64 x eps)) |
(-.f64 x eps) |
(pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(neg.f64 (sin.f64 x)) |
(sin.f64 x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.11659089903970274 | (sin.f64 (+.f64 eps x)) | |
| accuracy | 0.14374938459456219 | (sin.f64 (-.f64 x eps)) | |
| accuracy | 0.2109375 | (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) | |
| accuracy | 40.58914190290273 | (fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0 | (cos.f64 eps) | |
| accuracy | 0.0078125 | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) | |
| accuracy | 22.42661635599399 | (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) | |
| accuracy | 0 | (sin.f64 x) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.0078125 | (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) | |
| accuracy | 0.6457364923757021 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) | |
| accuracy | 0 | (sin.f64 eps) | |
| accuracy | 1.7867961863371942 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) | |
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.12592680321714567 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| 133.0ms | 222× | 1 | valid |
| 47.0ms | 26× | 2 | valid |
| 7.0ms | 3× | 3 | valid |
| 2.0ms | 5× | 0 | valid |
Compiled 420 to 82 computations (80.5% saved)
ival-sin: 52.0ms (34.2% of total)ival-mult: 31.0ms (20.4% of total)adjust: 26.0ms (17.1% of total)ival-add: 15.0ms (9.9% of total)ival-cos: 10.0ms (6.6% of total)ival-pow: 8.0ms (5.3% of total)ival-sub: 3.0ms (2% of total)ival-div: 2.0ms (1.3% of total)ival-neg: 2.0ms (1.3% of total)exact: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
#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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(sin.f64 x) |
(cos.f64 eps) |
(pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) |
(sin.f64 (-.f64 x eps)) |
| Outputs |
|---|
(* 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))))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(* x (- (cos eps) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1)) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* (sin eps) (sin (neg eps))) |
(+ (* x (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps)))) (* (sin eps) (sin (neg eps)))) |
(+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (* (cos eps) (cos (neg eps))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps)))) |
(+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (+ (* x (+ (* -1/2 (* (cos eps) (sin (neg eps)))) (+ (* -1/2 (* (cos (neg eps)) (sin eps))) (+ (* -1/6 (* (cos eps) (sin (neg eps)))) (* -1/6 (* (cos (neg eps)) (sin eps))))))) (* (cos eps) (cos (neg eps)))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps)))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+ eps x) |
(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)))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(/ 1 (sin (neg eps))) |
(+ (* -1 (/ (* x (cos (neg eps))) (pow (sin (neg eps)) 2))) (/ 1 (sin (neg eps)))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps)))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (+ (* 1/2 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (/ (* (cos (neg eps)) (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (sin (neg eps))))))) (* 1/2 (/ 1 (sin (neg eps))))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps)))) |
(sin (neg eps)) |
(+ (sin (neg eps)) (* x (cos (neg eps)))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps))))))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps))))))))) |
(* 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)))) |
(* -1/2 (sin x)) |
(- (* (cos eps) (sin x)) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(cos x) |
(* (sin (+ eps x)) (sin (- x eps))) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(sin x) |
(/ 1 (sin (- x eps))) |
(sin (- x eps)) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(/ 1 (sin (neg (+ eps (* -1 x))))) |
(sin (neg (+ 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)))) |
(* 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)) |
(* 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)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x))))))))) |
(pow (sin x) 2) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (sin x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (* -1 (pow (sin x) 2)))) (* (cos x) (sin x))))) (pow (sin x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (+ (* -1 (pow (sin x) 2)) (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* -1/6 (* (cos x) (sin x))) (+ (* 1/6 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x)))))))))) (* (cos x) (sin x))))) (pow (sin x) 2)) |
(+ (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)))))))) |
(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 (* -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)) |
(+ (/ 1 (sin x)) (/ (* eps (cos x)) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x))) (+ (* -1/2 (/ (cos x) (pow (sin x) 2))) (* 1/6 (/ (cos x) (pow (sin x) 2))))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(+ (sin x) (* -1 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x)))))))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(* (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 (/ x eps))) |
(cos 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))))) |
(* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(/ 1 (sin (+ x (* -1 eps)))) |
(sin (+ x (* -1 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | x | @ | inf | ((+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (cos eps) (sin x)) (neg (sin x))) (+ (* (sin eps) (cos x)) (+ (* (cos eps) (sin x)) (neg (sin x)))) (cos x) (+ (* (* (sin (+ eps x)) (sin (- x eps))) (pow (sin (- x eps)) -1)) (neg (sin x))) (* (sin (+ eps x)) (sin (- x eps))) (sin (+ eps x)) (+ eps x) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 (+ 0 eps)) (sin x) (cos eps) (pow (sin (- x eps)) -1) (sin (- x eps))) |
| 6.0ms | eps | @ | 0 | ((+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (cos eps) (sin x)) (neg (sin x))) (+ (* (sin eps) (cos x)) (+ (* (cos eps) (sin x)) (neg (sin x)))) (cos x) (+ (* (* (sin (+ eps x)) (sin (- x eps))) (pow (sin (- x eps)) -1)) (neg (sin x))) (* (sin (+ eps x)) (sin (- x eps))) (sin (+ eps x)) (+ eps x) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 (+ 0 eps)) (sin x) (cos eps) (pow (sin (- x eps)) -1) (sin (- x eps))) |
| 5.0ms | eps | @ | -inf | ((+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (cos eps) (sin x)) (neg (sin x))) (+ (* (sin eps) (cos x)) (+ (* (cos eps) (sin x)) (neg (sin x)))) (cos x) (+ (* (* (sin (+ eps x)) (sin (- x eps))) (pow (sin (- x eps)) -1)) (neg (sin x))) (* (sin (+ eps x)) (sin (- x eps))) (sin (+ eps x)) (+ eps x) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 (+ 0 eps)) (sin x) (cos eps) (pow (sin (- x eps)) -1) (sin (- x eps))) |
| 4.0ms | x | @ | 0 | ((+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (cos eps) (sin x)) (neg (sin x))) (+ (* (sin eps) (cos x)) (+ (* (cos eps) (sin x)) (neg (sin x)))) (cos x) (+ (* (* (sin (+ eps x)) (sin (- x eps))) (pow (sin (- x eps)) -1)) (neg (sin x))) (* (sin (+ eps x)) (sin (- x eps))) (sin (+ eps x)) (+ eps x) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 (+ 0 eps)) (sin x) (cos eps) (pow (sin (- x eps)) -1) (sin (- x eps))) |
| 4.0ms | x | @ | -inf | ((+ 0 eps) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (+ (* (cos eps) (sin x)) (neg (sin x))) (+ (* (sin eps) (cos x)) (+ (* (cos eps) (sin x)) (neg (sin x)))) (cos x) (+ (* (* (sin (+ eps x)) (sin (- x eps))) (pow (sin (- x eps)) -1)) (neg (sin x))) (* (sin (+ eps x)) (sin (- x eps))) (sin (+ eps x)) (+ eps x) (cos (/ (+ (* 2 x) eps) -2)) (* 1/2 (+ 0 eps)) (sin x) (cos eps) (pow (sin (- x eps)) -1) (sin (- x eps))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 547 | 1967 |
| 1 | 1706 | 1802 |
| 2 | 4973 | 1730 |
| 0 | 8093 | 1585 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 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))))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(* x (- (cos eps) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1)) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* (sin eps) (sin (neg eps))) |
(+ (* x (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps)))) (* (sin eps) (sin (neg eps)))) |
(+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (* (cos eps) (cos (neg eps))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps)))) |
(+ (* x (+ (* x (+ (* -1 (* (sin eps) (sin (neg eps)))) (+ (* x (+ (* -1/2 (* (cos eps) (sin (neg eps)))) (+ (* -1/2 (* (cos (neg eps)) (sin eps))) (+ (* -1/6 (* (cos eps) (sin (neg eps)))) (* -1/6 (* (cos (neg eps)) (sin eps))))))) (* (cos eps) (cos (neg eps)))))) (+ (* (cos eps) (sin (neg eps))) (* (cos (neg eps)) (sin eps))))) (* (sin eps) (sin (neg eps)))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+ eps x) |
(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)))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(/ 1 (sin (neg eps))) |
(+ (* -1 (/ (* x (cos (neg eps))) (pow (sin (neg eps)) 2))) (/ 1 (sin (neg eps)))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps)))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (+ (* 1/2 (/ (cos (neg eps)) (pow (sin (neg eps)) 2))) (/ (* (cos (neg eps)) (- (* 1/2 (/ 1 (sin (neg eps)))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (sin (neg eps))))))) (* 1/2 (/ 1 (sin (neg eps))))) (* -1 (/ (pow (cos (neg eps)) 2) (pow (sin (neg eps)) 3))))) (/ (cos (neg eps)) (pow (sin (neg eps)) 2)))) (/ 1 (sin (neg eps)))) |
(sin (neg eps)) |
(+ (sin (neg eps)) (* x (cos (neg eps)))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps))))))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps))))))))) |
(* 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)))) |
(* -1/2 (sin x)) |
(- (* (cos eps) (sin x)) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(cos x) |
(* (sin (+ eps x)) (sin (- x eps))) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(sin x) |
(/ 1 (sin (- x eps))) |
(sin (- x eps)) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (sin (neg (+ eps (* -1 x)))) (sin (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(/ 1 (sin (neg (+ eps (* -1 x))))) |
(sin (neg (+ 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)))) |
(* 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)) |
(* 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)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x))))))))) |
(pow (sin x) 2) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (sin x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (* -1 (pow (sin x) 2)))) (* (cos x) (sin x))))) (pow (sin x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (+ (* -1 (pow (sin x) 2)) (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* -1/6 (* (cos x) (sin x))) (+ (* 1/6 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x)))))))))) (* (cos x) (sin x))))) (pow (sin x) 2)) |
(+ (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)))))))) |
(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 (* -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)) |
(+ (/ 1 (sin x)) (/ (* eps (cos x)) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x))) (+ (* -1/2 (/ (cos x) (pow (sin x) 2))) (* 1/6 (/ (cos x) (pow (sin x) 2))))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(+ (sin x) (* -1 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x)))))))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(* (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 (/ x eps))) |
(cos 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))))) |
(* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(/ 1 (sin (+ x (* -1 eps)))) |
(sin (+ x (* -1 eps))) |
| Outputs |
|---|
(* 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 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.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 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.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)))))) |
(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 x eps)) eps) |
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1 |
#s(literal 1 binary64) |
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x |
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(cos x) |
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(* eps (+ 1 (* -1/24 (pow eps 2)))) |
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(* -1/2 (* (pow eps 2) (sin x))) |
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(pow (sin x) 2) |
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(fma.f64 (neg.f64 eps) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* -1 (pow (cos x) 2)) (+ (* -1 (pow (sin x) 2)) (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* -1/6 (* (cos x) (sin x))) (+ (* 1/6 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x)))))))))) (* (cos x) (sin x))))) (pow (sin x) 2)) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x))) eps #s(literal -1 binary64)) eps) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+ (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 #s(literal -1/2 binary64) (sin.f64 x)) eps (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 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)) |
(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 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.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 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(/ 1 (sin x)) |
(/.f64 #s(literal 1 binary64) (sin.f64 x)) |
(+ (/ 1 (sin x)) (/ (* eps (cos x)) (pow (sin x) 2))) |
(fma.f64 (cos.f64 x) (/.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal 1 binary64) (sin.f64 x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x))) (+ (* -1/2 (/ (cos x) (pow (sin x) 2))) (* 1/6 (/ (cos x) (pow (sin x) 2))))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (* -1 (/ (cos x) (pow (sin x) 2))))) (/ 1 (sin x))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 x))) (sin.f64 x)) (neg.f64 (cos.f64 x)) (/.f64 (*.f64 (cos.f64 x) #s(literal -1/3 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))) eps (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal 1 binary64) (sin.f64 x))) |
(+ (sin x) (* -1 (* eps (cos x)))) |
(fma.f64 (neg.f64 eps) (cos.f64 x) (sin.f64 x)) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (neg.f64 (cos.f64 x))) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* -1 (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 #s(literal -1/2 binary64) (sin.f64 x))) eps (neg.f64 (cos.f64 x))) eps (sin.f64 x)) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* (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) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(cos eps) |
(cos.f64 eps) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 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 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* (sin (+ x (* -1 eps))) (sin (- x (* -1 eps)))) |
(*.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 x eps))) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x eps) eps eps) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
(/ 1 (sin (+ x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) |
(sin (+ x (* -1 eps))) |
(sin.f64 (-.f64 x eps)) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 169 |
| 0 | 69 | 153 |
| 1 | 256 | 142 |
| 2 | 2132 | 142 |
| 0 | 10138 | 142 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
#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) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(sin.f64 x) |
(cos.f64 eps) |
(pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) |
(sin.f64 (-.f64 x eps)) |
| Outputs |
|---|
(*.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64))) |
(pow.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 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 (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 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)) #s(literal 0 binary64)) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64)) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (/.f64 (*.f64 eps eps) (neg.f64 eps))) |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #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 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.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) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 1 binary64) (sin.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)) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (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 (/.f64 (*.f64 eps eps) (neg.f64 eps)))) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (sin.f64 (/.f64 (*.f64 eps eps) (neg.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 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(*.f64 eps (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))) (*.f64 eps eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x))) |
(/.f64 (*.f64 eps (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (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 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x)) (neg.f64 eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (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 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x)) (*.f64 eps eps))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))) (neg.f64 eps))) |
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))) (*.f64 eps eps))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x)))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (neg.f64 eps) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))))) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (cos.f64 x)))) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (fma.f64 (pow.f64 (*.f64 eps (sin.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)))))) |
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(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))))) |
(fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))) |
(sin.f64 (-.f64 x eps)) |
(-.f64 (*.f64 (sin.f64 (-.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (*.f64 (cos.f64 (-.f64 x #s(literal 0 binary64))) (sin.f64 eps))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (+.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (+.f64 x eps)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (+.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (+.f64 x eps))))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (*.f64 eps (+.f64 x eps))))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x x (*.f64 eps (+.f64 x eps)))))) (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (*.f64 eps (+.f64 x eps))))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x x (*.f64 eps (+.f64 x eps))))))) |
(-.f64 (*.f64 (sin.f64 (-.f64 x eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (-.f64 x eps)) #s(literal 0 binary64))) |
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))) |
(exp.f64 (log.f64 (sin.f64 (-.f64 x eps)))) |
Compiled 21 888 to 2 442 computations (88.8% saved)
19 alts after pruning (16 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 652 | 14 | 666 |
| Fresh | 2 | 2 | 4 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 657 | 19 | 676 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 60.6% | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
| 99.8% | (fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))) | |
| 99.8% | (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) | |
| 99.7% | (fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (cos eps) (sin x)) (neg (sin x))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) | |
| 36.1% | (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))) | |
| ✓ | 60.6% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) | |
| ▶ | 99.6% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) |
| 99.4% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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)))) | |
| 99.0% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| 98.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| ▶ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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)) | |
| ▶ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| ✓ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) | |
| 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) | |
| ▶ | 99.8% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 833 to 581 computations (30.3% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 eps x) | |
| cost-diff | 0 | (sin.f64 (-.f64 eps x)) | |
| cost-diff | 0 | (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) | |
| cost-diff | 0 | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) | |
| cost-diff | 128 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 576 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 0 | (cos.f64 x) | |
| cost-diff | 0 | (*.f64 (cos.f64 x) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) | |
| cost-diff | 0 | (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| cost-diff | 128 | (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 333 |
| 0 | 95 | 323 |
| 1 | 152 | 323 |
| 2 | 304 | 323 |
| 3 | 562 | 323 |
| 4 | 934 | 323 |
| 5 | 1203 | 323 |
| 6 | 1683 | 323 |
| 7 | 2779 | 323 |
| 8 | 4490 | 321 |
| 9 | 5397 | 321 |
| 10 | 5549 | 321 |
| 11 | 6002 | 321 |
| 12 | 7428 | 321 |
| 13 | 7675 | 321 |
| 0 | 8023 | 311 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#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) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) |
(sin.f64 (-.f64 eps x)) |
(-.f64 eps x) |
eps |
x |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(literal 1/2 binary64) |
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))) |
(sin.f64 x) |
(+.f64 (cos.f64 eps) #s(literal -1 binary64)) |
(cos.f64 eps) |
#s(literal -1 binary64) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) |
(sin.f64 (-.f64 eps x)) |
(-.f64 eps x) |
eps |
x |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(literal 1/2 binary64) |
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))) |
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x)) |
(sin.f64 x) |
(+.f64 (cos.f64 eps) #s(literal -1 binary64)) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal -1 binary64) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.11659089903970274 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 0.14374938459456219 | (sin.f64 (-.f64 eps x)) | |
| accuracy | 25.007338800042508 | (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) | |
| accuracy | 30.32293529433152 | (+.f64 (cos.f64 eps) #s(literal -1 binary64)) | |
| accuracy | 0.00390625 | (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) | |
| accuracy | 0.12592680321714567 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.17670095803136265 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.00390625 | (*.f64 (cos.f64 x) eps) | |
| accuracy | 0.8576912026583888 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| accuracy | 0 | (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) | |
| accuracy | 0.6457364923757021 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) | |
| accuracy | 1.8046331883375046 | #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) | |
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.12592680321714567 | (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
| 210.0ms | 160× | 2 | valid |
| 62.0ms | 89× | 1 | valid |
| 4.0ms | 3× | 3 | valid |
| 2.0ms | 4× | 0 | valid |
Compiled 601 to 119 computations (80.2% saved)
adjust: 70.0ms (31.6% of total)ival-mult: 48.0ms (21.7% of total)ival-cos: 31.0ms (14% of total)const: 25.0ms (11.3% of total)ival-add: 18.0ms (8.1% of total)ival-sin: 18.0ms (8.1% of total)ival-sub: 6.0ms (2.7% of total)ival-div: 2.0ms (0.9% of total)exact: 1.0ms (0.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(/.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 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) |
(sin.f64 (-.f64 eps x)) |
(-.f64 eps x) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(+.f64 (cos.f64 eps) #s(literal -1 binary64)) |
(sin.f64 (+.f64 x eps)) |
| Outputs |
|---|
(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)))))) |
(* 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)))))))))) |
(* 2 (cos (* -1/2 eps))) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (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 (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (cos eps))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* -1/2 (* x (sin eps))) (* 1/2 (+ (cos eps) (* -1 (cos eps)))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) 1))) |
(* 2 (sin eps)) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* -1 (* x (sin eps))))))) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) |
(+ (sin eps) (* -1 (* x (cos eps)))) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* x (+ (* -1/2 (sin eps)) (* 1/6 (* x (cos eps)))))))) |
(+ eps (* -1 x)) |
(+ (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)))))))) |
(cos (- (* -1/2 eps) x)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (cos x)) |
(cos x) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (+ eps x)) (sin (- eps x))) |
(sin (- eps x)) |
(* x (- (/ eps x) 1)) |
(sin (+ eps x)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x)))) |
(sin (+ eps (* -1 x))) |
(* -1 (* x (+ 1 (* -1 (/ eps x))))) |
(sin (- eps (* -1 x))) |
(cos (neg x)) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg 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 (cos (neg x))) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) |
(* 2 (cos (neg x))) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg 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 (* -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 (+ 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)))) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x))))))))))) |
(+ (sin x) (sin (neg x))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (cos (neg x)))))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (+ (* -1/2 (sin (neg x))) (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x))))))))))))) |
(sin (neg x)) |
(+ (sin (neg x)) (* eps (cos (neg x)))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* -1/2 (* eps (sin (neg x))))))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* eps (+ (* -1/2 (sin (neg x))) (* -1/6 (* eps (cos (neg x))))))))) |
(- eps 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)))) |
-1/48 |
(- (* 1/3840 (pow eps 2)) 1/48) |
(* -1/2 (pow eps 2)) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(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)))))))) |
(cos (neg (+ x (* 1/2 eps)))) |
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps)))) |
(* 2 (cos (neg (+ x (* 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))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* eps (+ 1 (* -1 (/ x eps)))) |
(sin (* 1/2 eps)) |
(* 1/3840 (pow eps 2)) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(- (cos eps) 1) |
(* 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))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps)))) |
(sin (neg (+ x (* -1 eps)))) |
(* -1 (* eps (- (/ x eps) 1))) |
(sin (- x (* -1 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | eps | @ | 0 | ((cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (+ (sin (- eps x)) (sin (+ x eps))) (sin (- eps x)) (- eps x) (sin (* 1/2 eps)) (sin (* 1/2 (+ 0 eps))) (+ (* 1/3840 (* eps eps)) -1/48) (+ (cos eps) -1) (sin (+ x eps))) |
| 4.0ms | eps | @ | -inf | ((cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (+ (sin (- eps x)) (sin (+ x eps))) (sin (- eps x)) (- eps x) (sin (* 1/2 eps)) (sin (* 1/2 (+ 0 eps))) (+ (* 1/3840 (* eps eps)) -1/48) (+ (cos eps) -1) (sin (+ x eps))) |
| 4.0ms | eps | @ | inf | ((cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (+ (sin (- eps x)) (sin (+ x eps))) (sin (- eps x)) (- eps x) (sin (* 1/2 eps)) (sin (* 1/2 (+ 0 eps))) (+ (* 1/3840 (* eps eps)) -1/48) (+ (cos eps) -1) (sin (+ x eps))) |
| 4.0ms | x | @ | inf | ((cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (+ (sin (- eps x)) (sin (+ x eps))) (sin (- eps x)) (- eps x) (sin (* 1/2 eps)) (sin (* 1/2 (+ 0 eps))) (+ (* 1/3840 (* eps eps)) -1/48) (+ (cos eps) -1) (sin (+ x eps))) |
| 4.0ms | x | @ | -inf | ((cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (+ (sin (- eps x)) (sin (+ x eps))) (sin (- eps x)) (- eps x) (sin (* 1/2 eps)) (sin (* 1/2 (+ 0 eps))) (+ (* 1/3840 (* eps eps)) -1/48) (+ (cos eps) -1) (sin (+ x eps))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 527 | 1909 |
| 1 | 1729 | 1806 |
| 2 | 4477 | 1710 |
| 0 | 8289 | 1555 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(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)))))) |
(* 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)))))))))) |
(* 2 (cos (* -1/2 eps))) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (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 (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (cos eps))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* -1/2 (* x (sin eps))) (* 1/2 (+ (cos eps) (* -1 (cos eps)))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) 1))) |
(* 2 (sin eps)) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* -1 (* x (sin eps))))))) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) |
(+ (sin eps) (* -1 (* x (cos eps)))) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* x (+ (* -1/2 (sin eps)) (* 1/6 (* x (cos eps)))))))) |
(+ eps (* -1 x)) |
(+ (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)))))))) |
(cos (- (* -1/2 eps) x)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (cos x)) |
(cos x) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (+ eps x)) (sin (- eps x))) |
(sin (- eps x)) |
(* x (- (/ eps x) 1)) |
(sin (+ eps x)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x)))) |
(sin (+ eps (* -1 x))) |
(* -1 (* x (+ 1 (* -1 (/ eps x))))) |
(sin (- eps (* -1 x))) |
(cos (neg x)) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg 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 (cos (neg x))) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) |
(* 2 (cos (neg x))) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg 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 (* -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 (+ 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)))) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x))))))))))) |
(+ (sin x) (sin (neg x))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (cos (neg x)))))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (+ (* -1/2 (sin (neg x))) (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x))))))))))))) |
(sin (neg x)) |
(+ (sin (neg x)) (* eps (cos (neg x)))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* -1/2 (* eps (sin (neg x))))))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* eps (+ (* -1/2 (sin (neg x))) (* -1/6 (* eps (cos (neg x))))))))) |
(- eps 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)))) |
-1/48 |
(- (* 1/3840 (pow eps 2)) 1/48) |
(* -1/2 (pow eps 2)) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(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)))))))) |
(cos (neg (+ x (* 1/2 eps)))) |
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps)))) |
(* 2 (cos (neg (+ x (* 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))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* eps (+ 1 (* -1 (/ x eps)))) |
(sin (* 1/2 eps)) |
(* 1/3840 (pow eps 2)) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(- (cos eps) 1) |
(* 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))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps)))) |
(sin (neg (+ x (* -1 eps)))) |
(* -1 (* eps (- (/ x eps) 1))) |
(sin (- x (* -1 eps))) |
| Outputs |
|---|
(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 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.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 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (*.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 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(* 2 (cos (* -1/2 eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(*.f64 (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))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (neg.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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 (cos.f64 eps) #s(literal -1/6 binary64) #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 x eps)) 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 x eps)) #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 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (fma.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 (* -1/2 (* eps (pow x 2)))) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* -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)) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (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))) (* 1/2 (+ (cos eps) (* -1 (cos 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) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #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)) |
(* 2 (sin eps)) |
(*.f64 (sin.f64 eps) #s(literal 2 binary64)) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (* -1 (cos eps))))) |
(fma.f64 (sin.f64 eps) #s(literal 2 binary64) #s(literal 0 binary64)) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* -1 (* x (sin eps))))))) |
(fma.f64 (*.f64 (neg.f64 x) (sin.f64 eps)) x (*.f64 (sin.f64 eps) #s(literal 2 binary64))) |
(+ (* 2 (sin eps)) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) |
(fma.f64 (*.f64 (neg.f64 x) (sin.f64 eps)) x (*.f64 (sin.f64 eps) #s(literal 2 binary64))) |
(+ (sin eps) (* -1 (* x (cos eps)))) |
(fma.f64 (neg.f64 (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 eps) (neg.f64 (cos.f64 eps))) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (* -1 (cos eps)) (* x (+ (* -1/2 (sin eps)) (* 1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (neg.f64 (cos.f64 eps))) x (sin.f64 eps)) |
(+ eps (* -1 x)) |
(-.f64 eps x) |
(+ (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 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
(cos (- (* -1/2 eps) x)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps 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))) |
(* 2 (* (cos (- (* -1/2 eps) 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))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (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)) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(cos x) |
(cos.f64 x) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(+ (sin (+ eps x)) (sin (- eps x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) |
(sin (- eps x)) |
(sin.f64 (-.f64 eps x)) |
(* x (- (/ eps x) 1)) |
(fma.f64 (/.f64 eps x) x (neg.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps 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))) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 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))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) |
(sin (+ eps (* -1 x))) |
(sin.f64 (-.f64 eps x)) |
(* -1 (* x (+ 1 (* -1 (/ eps x))))) |
(fma.f64 (/.f64 eps x) x (neg.f64 x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(cos (neg x)) |
(cos.f64 x) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x)) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* 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 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.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) |
(* eps (cos (neg x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg 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) |
(* 2 (cos (neg x))) |
(*.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg x))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.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 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(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 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) 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 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* 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)) (fma.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 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
#s(literal 0 binary64) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(fma.f64 (cos.f64 x) eps #s(literal 0 binary64)) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps #s(literal 0 binary64)) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/3 binary64)) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps #s(literal 0 binary64)) |
(+ (sin x) (sin (neg x))) |
#s(literal 0 binary64) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (cos (neg x)))))) |
(fma.f64 (*.f64 (cos.f64 x) #s(literal 2 binary64)) eps #s(literal 0 binary64)) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(fma.f64 (fma.f64 #s(literal 0 binary64) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) eps #s(literal 0 binary64)) |
(+ (sin x) (+ (sin (neg x)) (* eps (+ (cos x) (+ (cos (neg x)) (* eps (+ (* -1/2 (sin x)) (+ (* -1/2 (sin (neg x))) (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x))))))))))))) |
(fma.f64 (fma.f64 (cos.f64 x) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/3 binary64)) eps #s(literal 0 binary64)) eps)) eps #s(literal 0 binary64)) |
(sin (neg x)) |
(neg.f64 (sin.f64 x)) |
(+ (sin (neg x)) (* eps (cos (neg x)))) |
(fma.f64 (cos.f64 x) eps (neg.f64 (sin.f64 x))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* -1/2 (* eps (sin (neg x))))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(+ (sin (neg x)) (* eps (+ (cos (neg x)) (* eps (+ (* -1/2 (sin (neg x))) (* -1/6 (* eps (cos (neg x))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(- eps x) |
(-.f64 eps x) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
-1/48 |
#s(literal -1/48 binary64) |
(- (* 1/3840 (pow eps 2)) 1/48) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) eps) eps) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (*.f64 eps eps) #s(literal -1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(sin x) |
(sin.f64 x) |
(+ (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 #s(literal -1/2 binary64) (sin.f64 x)) eps (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 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)) |
(cos (neg (+ x (* 1/2 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* 2 (* (cos (neg (+ x (* 1/2 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))) |
(* 2 (cos (neg (+ x (* 1/2 eps))))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(* -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 (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 #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) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(* eps (+ 1 (* -1 (/ x eps)))) |
(fma.f64 (/.f64 (neg.f64 x) eps) eps eps) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* 1/3840 (pow eps 2)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(*.f64 (*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) eps) eps) |
(- (cos eps) 1) |
(-.f64 (cos.f64 eps) #s(literal 1 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 (- 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 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) |
(sin (neg (+ x (* -1 eps)))) |
(sin.f64 (-.f64 eps x)) |
(* -1 (* eps (- (/ x eps) 1))) |
(fma.f64 (/.f64 (neg.f64 x) eps) eps eps) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 257 |
| 0 | 95 | 249 |
| 1 | 322 | 249 |
| 2 | 2520 | 249 |
| 0 | 8581 | 246 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(/.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 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) |
(sin.f64 (-.f64 eps x)) |
(-.f64 eps x) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(+.f64 (cos.f64 eps) #s(literal -1 binary64)) |
(sin.f64 (+.f64 x eps)) |
| Outputs |
|---|
(/.f64 (fma.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) #s(literal 4 binary64)) |
(/.f64 (fma.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x)) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))))) #s(literal 4 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64))) (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) x))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) x))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) x))))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x))) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal -1/2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x)))) |
(cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) x))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) x)))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (fma.f64 eps #s(literal -1/2 binary64) x))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal -1/2 binary64) x))))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x)))))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(literal -1/2 binary64) x))))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(*.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal 2 binary64)) |
(fma.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) |
(+.f64 (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
(*.f64 eps #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))) (*.f64 eps eps)) |
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(fma.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)))) |
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(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
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(/.f64 (fma.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 eps x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 x eps))))) #s(literal 4 binary64)) |
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 x eps))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 eps x))))) #s(literal 4 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 x eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))))) |
(fma.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps) (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) (cos.f64 (+.f64 #s(literal 0 binary64) x)) (*.f64 (cos.f64 eps) (sin.f64 (+.f64 #s(literal 0 binary64) x)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 (+.f64 x eps)) #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)) (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps)))) |
(sin.f64 (+.f64 x eps)) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(+.f64 (*.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps))) |
(+.f64 (*.f64 (sin.f64 (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps)))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 (+.f64 #s(literal 0 binary64) x))) (*.f64 (cos.f64 eps) (sin.f64 (+.f64 #s(literal 0 binary64) x)))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) |
Compiled 17 656 to 1 913 computations (89.2% saved)
25 alts after pruning (19 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 437 | 11 | 448 |
| Fresh | 3 | 8 | 11 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 442 | 25 | 467 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 60.6% | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
| 60.4% | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(approx (+ (cos eps) -1) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) | |
| 99.8% | (fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))) | |
| 99.8% | (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) | |
| 99.7% | (fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (cos eps) (sin x)) (neg (sin x))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) | |
| 36.1% | (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))) | |
| ✓ | 60.6% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| 98.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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)) | |
| ✓ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| 98.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| ▶ | 97.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| ✓ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) | |
| 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) | |
| ▶ | 5.2% | #s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
| ▶ | 100.0% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
| ▶ | 99.8% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
| 99.7% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) | |
| 99.4% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) | |
| ▶ | 99.0% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 1 216 to 851 computations (30% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| cost-diff | 0 | (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.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))) | |
| cost-diff | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) | |
| cost-diff | 0 | (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) | |
| cost-diff | 128 | (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) | |
| cost-diff | 0 | (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | #s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) | |
| cost-diff | 0 | (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) | |
| cost-diff | 0 | (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 384 |
| 0 | 93 | 380 |
| 1 | 154 | 380 |
| 2 | 257 | 380 |
| 3 | 439 | 380 |
| 4 | 770 | 374 |
| 5 | 1121 | 374 |
| 6 | 1578 | 374 |
| 7 | 2320 | 374 |
| 8 | 3267 | 365 |
| 9 | 4363 | 365 |
| 10 | 5307 | 365 |
| 11 | 5989 | 365 |
| 12 | 7073 | 365 |
| 13 | 7543 | 365 |
| 14 | 7774 | 365 |
| 0 | 8232 | 364 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
(cos.f64 (*.f64 eps #s(literal -1/2 binary64))) |
(*.f64 eps #s(literal -1/2 binary64)) |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
x |
(*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) |
(sin.f64 (*.f64 eps #s(literal -1/2 binary64))) |
(sin.f64 x) |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
#s(literal 1/24 binary64) |
(*.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
(*.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))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
#s(literal 1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(cos.f64 (*.f64 eps #s(literal -1/2 binary64))) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 eps #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) eps) |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
x |
(*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) |
(*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(sin.f64 (*.f64 eps #s(literal -1/2 binary64))) |
(sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(sin.f64 x) |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) |
#s(literal 1/24 binary64) |
(*.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) 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))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) | |
| accuracy | 0.0078125 | (*.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))) | |
| accuracy | 0.12592680321714567 | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| accuracy | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.12592680321714567 | (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) | |
| accuracy | 0.6148686422748073 | #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0.00390625 | (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) | |
| accuracy | 0.8576912026583888 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| accuracy | 1.3469485712837066 | #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 60.672664010527505 | #s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0 | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.015625 | (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) |
| 245.0ms | 216× | 0 | valid |
| 26.0ms | 40× | 1 | valid |
Compiled 676 to 127 computations (81.2% saved)
ival-mult: 64.0ms (57.1% of total)ival-cos: 12.0ms (10.7% of total)ival-add: 12.0ms (10.7% of total)ival-sin: 10.0ms (8.9% of total)adjust: 5.0ms (4.5% of total)const: 4.0ms (3.6% of total)ival-sub: 3.0ms (2.7% of total)ival-div: 2.0ms (1.8% of total)exact: 1.0ms (0.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
(*.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))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) |
(cos.f64 x) |
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| Outputs |
|---|
(* 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)))))))))) |
(* 2 (cos (* -1/2 eps))) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps))))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* -1/2 eps))))))) |
(+ (cos (* -1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (cos eps))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* -1/2 (* x (sin eps))) (* 1/2 (+ (cos eps) (* -1 (cos eps)))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) 1))) |
(+ (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 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ (cos (* -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)))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (cos (* 1/2 eps))) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(* x (sin (* -1/2 eps))) |
(* x (+ (sin (* -1/2 eps)) (* -1/6 (* (pow x 2) (sin (* -1/2 eps)))))) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* 1/120 (* (pow x 2) (sin (* -1/2 eps)))))))) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/120 (sin (* -1/2 eps))))))))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))) |
(* 2 (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps))))) |
(+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* 1/24 (pow x 4)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(cos (- (* -1/2 eps) x)) |
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(cos (+ x (* 1/2 eps))) |
(* (sin x) (sin (* -1/2 eps))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(cos (- (* 1/2 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 (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (cos x)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg 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 (neg x)) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) |
(* eps (cos (neg x))) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) |
(* 2 (cos (neg x))) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg x))))))))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x)))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin 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)))) |
(cos (neg (+ x (* 1/2 eps)))) |
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps)))) |
(* 2 (cos (neg (+ x (* 1/2 eps))))) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(cos (- x (* -1/2 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 53.0ms | eps | @ | inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (sin (* 1/2 eps))) (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (sin (* eps -1/2)) (sin x)) (cos x) (sin (* 1/2 eps)) (sin (* 1/2 eps))) |
| 6.0ms | x | @ | inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (sin (* 1/2 eps))) (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (sin (* eps -1/2)) (sin x)) (cos x) (sin (* 1/2 eps)) (sin (* 1/2 eps))) |
| 5.0ms | x | @ | -inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (sin (* 1/2 eps))) (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (sin (* eps -1/2)) (sin x)) (cos x) (sin (* 1/2 eps)) (sin (* 1/2 eps))) |
| 4.0ms | eps | @ | -inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (sin (* 1/2 eps))) (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (sin (* eps -1/2)) (sin x)) (cos x) (sin (* 1/2 eps)) (sin (* 1/2 eps))) |
| 3.0ms | x | @ | 0 | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (sin (* 1/2 eps))) (* (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) 2) (+ (* (cos (* eps -1/2)) (cos x)) (* (sin (* eps -1/2)) (sin x))) (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1) (cos (- (* -1/2 eps) x)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (- (* -1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (- (* -1/2 eps) x)) 2) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (* (sin (* eps -1/2)) (sin x)) (cos x) (sin (* 1/2 eps)) (sin (* 1/2 eps))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 521 | 2028 |
| 1 | 1716 | 1854 |
| 2 | 4420 | 1757 |
| 0 | 8669 | 1594 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 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)))))))))) |
(* 2 (cos (* -1/2 eps))) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps))))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* -1/2 eps))))))) |
(+ (cos (* -1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (cos eps))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* -1/2 (* x (sin eps))) (* 1/2 (+ (cos eps) (* -1 (cos eps)))))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 1/6 (cos eps)))))))))) 1))) |
(+ (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 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ (cos (* -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)))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (cos (* 1/2 eps))) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(* x (sin (* -1/2 eps))) |
(* x (+ (sin (* -1/2 eps)) (* -1/6 (* (pow x 2) (sin (* -1/2 eps)))))) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* 1/120 (* (pow x 2) (sin (* -1/2 eps)))))))) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/120 (sin (* -1/2 eps))))))))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))) |
(* 2 (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps))))) |
(+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* 1/24 (pow x 4)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(cos (- (* -1/2 eps) x)) |
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(cos (+ x (* 1/2 eps))) |
(* (sin x) (sin (* -1/2 eps))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(cos (- (* 1/2 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 (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (cos x)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg 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 (neg x)) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) |
(* eps (cos (neg x))) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) |
(* 2 (cos (neg x))) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg x))))))))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x)))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin 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)))) |
(cos (neg (+ x (* 1/2 eps)))) |
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps)))) |
(* 2 (cos (neg (+ x (* 1/2 eps))))) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(cos (- x (* -1/2 eps))) |
| Outputs |
|---|
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.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 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) 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))))))) |
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) x) #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 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (fma.f64 x (*.f64 #s(literal -1/3 binary64) x) #s(literal 2 binary64)))) x)) |
(* 2 (cos (* -1/2 eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* 2 (cos (* -1/2 eps))) (* 2 (* x (sin (* -1/2 eps))))) |
(*.f64 (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))) (* x (+ (* -1 (* x (cos (* -1/2 eps)))) (* 2 (sin (* -1/2 eps)))))) |
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (neg.f64 x) x #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x #s(literal 2 binary64)))) |
(+ (* 2 (cos (* -1/2 eps))) (* x (+ (* 2 (sin (* -1/2 eps))) (* x (+ (* -1 (cos (* -1/2 eps))) (* -1/3 (* x (sin (* -1/2 eps))))))))) |
(fma.f64 (fma.f64 (neg.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 x (*.f64 #s(literal -1/3 binary64) x) #s(literal 2 binary64)))) x (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))) |
(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 (+ (sin (* -1/2 eps)) (* -1/2 (* x (cos (* -1/2 eps))))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(+ (cos (* -1/2 eps)) (* x (+ (sin (* -1/2 eps)) (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (+ (cos eps) (* 1/2 (+ (cos eps) (* -1 (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))) (* 1/2 (+ (cos eps) (* -1 (cos eps)))))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (+ (* 1/2 (+ (cos eps) (* -1 (cos eps)))) (* x (+ (* -1/2 (sin eps)) (* x (+ (* -1/6 (- (cos eps) 1)) (* 1/2 (+ (* -1/6 (cos eps)) (* 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)) |
(+ (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) #s(literal -1/2 binary64)) x (-.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 (* eps (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 x x) eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (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 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 (*.f64 #s(literal -2 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(fma.f64 (*.f64 #s(literal -2 binary64) x) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 2 binary64)))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) x) #s(literal -2 binary64)))) x)) |
(* 2 (cos (* 1/2 eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(fma.f64 (*.f64 #s(literal -2 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(fma.f64 (*.f64 #s(literal -2 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (neg.f64 x) x #s(literal 2 binary64)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (neg.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (*.f64 #s(literal 1/3 binary64) x) #s(literal -2 binary64)))) x (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* 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)))) (sin (* 1/2 eps))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (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)))))) (sin (* 1/2 eps))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (*.f64 #s(literal 1/6 binary64) x) #s(literal -1 binary64)))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* x (sin (* -1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) |
(* x (+ (sin (* -1/2 eps)) (* -1/6 (* (pow x 2) (sin (* -1/2 eps)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 x (*.f64 (*.f64 #s(literal -1/6 binary64) x) x) x)) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* 1/120 (* (pow x 2) (sin (* -1/2 eps)))))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x) |
(* x (+ (sin (* -1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* -1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* -1/2 eps)))) (* 1/120 (sin (* -1/2 eps))))))))) |
(*.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))))) x) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x)))) |
(* 2 (+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps))))) |
(*.f64 (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) |
(+ (* (cos x) (cos (* -1/2 eps))) (* (sin x) (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x))) |
(+ (* 1/2 (+ (sin (+ eps x)) (sin (- eps x)))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(cos x) |
(cos.f64 x) |
(* 1/24 (pow x 4)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) |
(cos (- (* -1/2 eps) x)) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (- (* -1/2 eps) x))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* (sin x) (sin (* -1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* 1/2 (+ (sin (+ eps (* -1 x))) (sin (- eps (* -1 x))))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(cos (+ (* -1 x) (* -1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (+ (* -1 x) (* -1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* 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) eps) #s(literal -1/6 binary64) (*.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 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 #s(literal -1/24 binary64) eps))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(* 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) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(* 2 (cos x)) |
(*.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal -1/4 binary64) eps) #s(literal 2 binary64)))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))) |
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) |
(* 1/2 (+ (sin x) (sin (neg x)))) |
#s(literal 0 binary64) |
(+ (* 1/2 (* eps (+ (cos x) (cos (neg x))))) (* 1/2 (+ (sin x) (sin (neg x))))) |
(fma.f64 (cos.f64 x) eps #s(literal 0 binary64)) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x)))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps #s(literal 0 binary64)) |
(+ (* 1/2 (+ (sin x) (sin (neg x)))) (* eps (+ (* 1/2 (+ (cos x) (cos (neg x)))) (* eps (+ (* -1/2 (sin x)) (+ (* 1/2 (* eps (+ (* -1/6 (cos x)) (* -1/6 (cos (neg x)))))) (* 1/2 (+ (* -1/2 (sin x)) (* -1/2 (sin (neg x))))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/3 binary64)) eps (neg.f64 (sin.f64 x)))) eps (cos.f64 x)) eps #s(literal 0 binary64)) |
(* 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 #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 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(cos (neg x)) |
(cos.f64 x) |
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (cos.f64 x)) |
(* eps (cos (neg x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) |
(*.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 #s(literal -1/24 binary64) eps))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(* 2 (cos (neg x))) |
(*.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* 2 (cos (neg x))) (* eps (sin (neg x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* -1/4 (* eps (cos (neg x))))))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal -1/4 binary64) eps) #s(literal 2 binary64)))) |
(+ (* 2 (cos (neg x))) (* eps (+ (sin (neg x)) (* eps (+ (* -1/4 (cos (neg x))) (* -1/24 (* eps (sin (neg x))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x))))) |
(*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64))) eps) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x)))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/3840 binary64) (*.f64 eps eps) #s(literal 1/48 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin x))))))))) |
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/48 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (sin.f64 x) (fma.f64 #s(literal 1/645120 binary64) (*.f64 eps eps) #s(literal -1/3840 binary64))))) eps) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(cos (neg (+ x (* 1/2 eps)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (neg (+ x (* 1/2 eps))))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* 1/2 (+ (sin (neg (+ x (* -1 eps)))) (sin (- x (* -1 eps))))) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (sin.f64 x))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(cos (- x (* -1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 317 |
| 0 | 93 | 279 |
| 1 | 351 | 279 |
| 2 | 2649 | 279 |
| 0 | 8583 | 275 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
(*.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))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x)) |
(cos.f64 x) |
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) |
(/.f64 (*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
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(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
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(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) eps x))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) eps x)))))) (*.f64 (sin.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) eps x))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) eps x))))))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(+.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) |
(*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps)))) |
(/.f64 (*.f64 (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) |
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) |
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
(+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(+.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(/.f64 (-.f64 (+.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (-.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (*.f64 (sin.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))))) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x))) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) |
(-.f64 (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 #s(literal 0 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (cos.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x))))) (*.f64 (sin.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))) (sin.f64 (/.f64 (*.f64 x x) (fma.f64 eps #s(literal 1/2 binary64) (neg.f64 x)))))) |
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) |
(*.f64 (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) #s(literal 1/2 binary64)) |
(*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) |
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)))) #s(literal -2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x))))) |
(-.f64 (/.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps x)) #s(literal 2 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
Compiled 12 139 to 1 333 computations (89% saved)
25 alts after pruning (15 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 271 | 2 | 273 |
| Fresh | 1 | 13 | 14 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 6 | 6 |
| Total | 273 | 25 | 298 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 60.6% | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
| 60.4% | (fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(approx (+ (cos eps) -1) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) | |
| 99.8% | (fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))) | |
| 99.8% | (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) | |
| 99.7% | (fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (cos eps) (sin x)) (neg (sin x))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) | |
| 36.1% | (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))) | |
| ✓ | 60.6% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| ✓ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| 98.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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)) | |
| ✓ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| 98.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| ✓ | 97.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| ✓ | 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| 97.6% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) | |
| 97.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) | |
| ✓ | 5.2% | #s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
| ✓ | 100.0% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
| ✓ | 99.8% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
| 99.7% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) | |
| 99.4% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) | |
| 99.0% | #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 1 605 to 685 computations (57.3% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(approx (+ (cos eps) -1) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (cos eps) (sin x)) (neg (sin x))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x))))) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
3 calls:
| 10.0ms | eps |
| 10.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 10.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(approx (+ (cos eps) -1) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (+ (* (cos eps) (sin x)) (neg (sin x))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (sin.f64 x)))) |
(fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) (pow.f64 (sin.f64 (-.f64 x eps)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
3 calls:
| 10.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 9.0ms | x |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
3 calls:
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
| 99.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #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)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 7.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | x |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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)))) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
3 calls:
| 6.0ms | x |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
| 99.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.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)))) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
3 calls:
| 4.0ms | x |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.0% | 1 | x |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) 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 (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
3 calls:
| 5.0ms | eps |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
| 98.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | eps |
| 98.1% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) (fma.f64 (fma.f64 (fma.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)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
3 calls:
| 3.0ms | eps |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | eps |
| 97.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.9% | 1 | x |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.2% | 1 | x |
| 97.2% | 1 | eps |
| 97.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.2% | 1 | x |
| 5.2% | 1 | eps |
| 5.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 121 | 393 |
| 1 | 151 | 393 |
| 2 | 154 | 393 |
| 3 | 156 | 393 |
| 4 | 157 | 393 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal -1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) #s(literal 2 binary64)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.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)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (*.f64 (cos.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) #s(literal 2 binary64)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(approx (cos (- (* -1/2 eps) x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (+.f64 x eps) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (sin (- eps x)) (sin (+ x eps))) 1/2) (* (sin x) (+ (cos eps) -1))) #s(literal 0 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 0 | 521 | 2028 |
| 1 | 1716 | 1854 |
| 2 | 4420 | 1757 |
| 0 | 8669 | 1594 |
| 0 | 547 | 1967 |
| 1 | 1706 | 1802 |
| 2 | 4973 | 1730 |
| 0 | 8093 | 1585 |
| 0 | 39 | 169 |
| 0 | 69 | 153 |
| 1 | 256 | 142 |
| 2 | 2132 | 142 |
| 0 | 10138 | 142 |
| 0 | 107 | 291 |
| 1 | 314 | 291 |
| 2 | 779 | 284 |
| 3 | 2842 | 284 |
| 4 | 6177 | 284 |
| 0 | 8125 | 253 |
| 0 | 527 | 1909 |
| 1 | 1729 | 1806 |
| 2 | 4477 | 1710 |
| 0 | 8289 | 1555 |
| 0 | 62 | 257 |
| 0 | 95 | 249 |
| 1 | 322 | 249 |
| 2 | 2520 | 249 |
| 0 | 8581 | 246 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 635 to 326 computations (48.7% saved)
Compiled 830 to 286 computations (65.5% saved)
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