
Time bar (total: 14.4s)
| 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)
| 3.0s | 25 866× | 0 | invalid |
| 940.0ms | 5 514× | 0 | valid |
| 532.0ms | 2 742× | 1 | valid |
ival-mult: 670.0ms (19.7% of total)const: 594.0ms (17.5% of total)ival-sin: 580.0ms (17.1% of total)ival-add: 316.0ms (9.3% of total)ival-fabs: 288.0ms (8.5% of total)ival-<: 257.0ms (7.6% of total)ival-<=: 227.0ms (6.7% of total)ival-sub: 219.0ms (6.5% of total)ival-and: 104.0ms (3.1% of total)adjust: 81.0ms (2.4% of total)exact: 46.0ms (1.4% of total)ival-assert: 13.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 221 | 4 | (-4.4038464755470124e-32 1.6329471573534814e-34) | 4 | (-2.367090113444104e-117 2.741910301514028e-119) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 0 | 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 | 221 | 9 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 217 | 4 |
| - | 4 | 31 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 217 | 4 | 0 |
| - | 4 | 5 | 26 |
| number | freq |
|---|---|
| 0 | 35 |
| 1 | 221 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 22.0ms | 182× | 1 | valid |
| 20.0ms | 326× | 0 | valid |
| 2.0ms | 4× | 2 | valid |
Compiled 49 to 22 computations (55.1% saved)
ival-sin: 11.0ms (44.2% of total)adjust: 8.0ms (32.1% of total)ival-add: 3.0ms (12.1% of total)ival-sub: 3.0ms (12.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
| 102× | sub-neg |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 68× | cancel-sign-sub-inv |
| 64× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 6 computations (33.3% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.1% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (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)) |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 36× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (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)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
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 | 0.028601281620653757 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 24.210456116733425 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 20.0ms | 91× | 1 | valid |
| 8.0ms | 163× | 0 | valid |
| 1.0ms | 2× | 2 | valid |
Compiled 20 to 8 computations (60% saved)
adjust: 11.0ms (56.2% of total)ival-sin: 5.0ms (25.6% of total)ival-add: 2.0ms (10.2% of total)ival-sub: 1.0ms (5.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (sin.f64 x)> |
| Outputs |
|---|
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (sin x)> |
#<alt (+ (sin x) (* eps (cos x)))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (cos eps)))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | eps | @ | 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)) |
| 0.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1× | egg-herbie |
| 16 678× | lower-fma.f64 |
| 16 678× | lower-fma.f32 |
| 4 132× | lower-*.f64 |
| 4 132× | lower-*.f32 |
| 2 614× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2829 | 489 |
| 4 | 6198 | 489 |
| 0 | 8141 | 458 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 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) |
(+ (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)))))))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(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) |
(+ (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) |
(+ eps x) |
(+ 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)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps))) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 eps (cos.f64 x) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps 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 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 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)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(-.f64 (fma.f64 x (cos.f64 eps) (sin.f64 eps)) x) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (cos.f64 eps))) x) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) x) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 x (cos.f64 eps) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 (cos.f64 eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 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 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps 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)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
| 4 986× | lower-fma.f64 |
| 4 986× | lower-fma.f32 |
| 4 676× | lower-*.f64 |
| 4 676× | lower-*.f32 |
| 2 176× | lower-/.f64 |
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 |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64))) |
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (neg.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(+.f64 (sin.f64 (neg.f64 x)) (sin.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) |
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x)) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) (sin.f64 (neg.f64 x))) |
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps))) |
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (neg.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (/.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (-.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (pow.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) #s(literal 1 binary64)) (sin.f64 (neg.f64 x))) |
(fma.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64)) (sin.f64 (neg.f64 x))) |
(neg.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (neg.f64 (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))) |
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (neg.f64 x)))))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
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(*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x)))))) |
(*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) |
(*.f64 (pow.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))) #s(literal -1 binary64))) |
(+.f64 x eps) |
(+.f64 eps x) |
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(neg.f64 (/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (*.f64 eps eps)) (-.f64 x eps))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps)))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps)))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) |
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64))) |
(sin.f64 x) |
(pow.f64 (sin.f64 x) #s(literal 1 binary64)) |
Compiled 7 823 to 844 computations (89.2% saved)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 281 | 10 | 291 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 281 | 11 | 292 |
| Status | Accuracy | Program |
|---|---|---|
| 7.0% | (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) | |
| ✓ | 62.1% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ▶ | 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
| ▶ | 60.8% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))) | |
| ▶ | 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
| 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) | |
| ▶ | 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 385 to 236 computations (38.7% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) | |
| cost-diff | 0 | (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) | |
| cost-diff | 0 | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) | |
| cost-diff | 0 | #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| cost-diff | 0 | #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 192 | (+.f64 eps #s(literal 0 binary64)) | |
| cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| 10 866× | lower-fma.f32 |
| 10 852× | lower-fma.f64 |
| 4 398× | lower-*.f32 |
| 4 376× | lower-*.f64 |
| 1 816× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 330 |
| 0 | 82 | 304 |
| 1 | 144 | 304 |
| 2 | 321 | 304 |
| 3 | 706 | 300 |
| 4 | 1522 | 300 |
| 5 | 3580 | 300 |
| 6 | 4475 | 300 |
| 7 | 4675 | 300 |
| 8 | 4776 | 300 |
| 9 | 4808 | 300 |
| 10 | 4954 | 300 |
| 11 | 5937 | 300 |
| 12 | 6308 | 300 |
| 13 | 6852 | 300 |
| 14 | 7299 | 300 |
| 15 | 7468 | 300 |
| 16 | 7953 | 300 |
| 0 | 8034 | 293 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
#s(literal 0 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(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 |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
(*.f64 x x) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
eps |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
x |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(cos.f64 x) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
eps |
#s(literal 0 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(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 |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x))) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)) |
#s(approx (sin x) (fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x)) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x) |
(fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x))) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)) |
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
(*.f64 x x) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
eps |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
(fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
x |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(cos.f64 x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| accuracy | 0.01171875 | (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) | |
| accuracy | 0.19435856945876126 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) | |
| accuracy | 0.37890625 | (*.f64 eps #s(literal -1/6 binary64)) | |
| accuracy | 0.09375 | (*.f64 x (*.f64 x x)) | |
| accuracy | 0.1015625 | (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) | |
| accuracy | 0.5550165482334896 | #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| accuracy | 24.210456116733425 | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| accuracy | 0.028601281620653757 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 0.09375 | (*.f64 x (*.f64 x x)) | |
| accuracy | 0.9491102518809771 | #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)) | |
| accuracy | 24.210456116733425 | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) | |
| accuracy | 0 | (sin.f64 eps) | |
| accuracy | 1.6931742966796064 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| accuracy | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| accuracy | 0 | (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| accuracy | 0.04096027073711682 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| 61.0ms | 90× | 1 | valid |
| 58.0ms | 164× | 0 | valid |
| 2.0ms | 2× | 2 | valid |
Compiled 274 to 46 computations (83.2% saved)
ival-mult: 40.0ms (43% of total)ival-add: 16.0ms (17.2% of total)const: 14.0ms (15% of total)adjust: 8.0ms (8.6% of total)ival-sin: 8.0ms (8.6% of total)ival-cos: 4.0ms (4.3% of total)ival-sub: 2.0ms (2.1% of total)exact: 1.0ms (1.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (+.f64 eps #s(literal 0 binary64))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))> |
#<alt (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))> |
#<alt (sin.f64 eps)> |
#<alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))> |
#<alt (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)))> |
#<alt #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))> |
#<alt (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))> |
#<alt (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))> |
#<alt (*.f64 #s(literal -1/2 binary64) (sin.f64 x))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))> |
#<alt (*.f64 x (*.f64 x x))> |
#<alt (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))> |
#<alt (*.f64 eps #s(literal -1/6 binary64))> |
| Outputs |
|---|
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (sin x)> |
#<alt (+ (sin x) (* eps (cos x)))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (cos eps)))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (* 1/120 x)> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (* -1/5040 (pow x 3))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (* -1/5040 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 9.0ms | x | @ | inf | ((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6)) |
| 4.0ms | x | @ | -inf | ((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6)) |
| 3.0ms | eps | @ | inf | ((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6)) |
| 3.0ms | eps | @ | 0 | ((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6)) |
| 3.0ms | x | @ | 0 | ((* (+ (* x 2) eps) 1/2) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (cos (* (+ (* x 2) eps) 1/2)) (sin (* (+ eps 0) 1/2)) (* x (* x x)) (* x (+ (* (* x x) -1/5040) 1/120)) (* eps -1/6)) |
| 1× | egg-herbie |
| 15 108× | lower-fma.f64 |
| 15 108× | lower-fma.f32 |
| 5 974× | lower-*.f64 |
| 5 974× | lower-*.f32 |
| 4 464× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 379 | 3701 |
| 1 | 1190 | 3521 |
| 2 | 3339 | 3483 |
| 0 | 8299 | 3200 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
eps |
eps |
eps |
eps |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* 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))))))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(* 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) |
(+ (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)))))))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(* 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))))))))) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin 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) |
(* 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)))) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 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))) |
(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) |
(+ (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) |
(+ eps x) |
(+ 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) |
(+ (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))) |
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) |
(+ (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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(* -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)) |
(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))))) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(* 1/120 x) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(* -1/5040 (pow x 3)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(* -1/5040 (pow x 3)) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
| Outputs |
|---|
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
eps |
eps |
eps |
eps |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 eps (cos.f64 x) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 eps (cos.f64 x) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 eps (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) |
x |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (cos.f64 x) (*.f64 eps eps))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (cos.f64 x) (*.f64 eps eps))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(*.f64 (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(*.f64 (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(*.f64 eps (*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(*.f64 eps (*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
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(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* -1/6 eps) |
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(* -1/6 eps) |
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(* -1/6 eps) |
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(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 x #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))) |
(fma.f64 x (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (neg.f64 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 x (fma.f64 x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (fma.f64 x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (fma.f64 x (cos.f64 eps) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (fma.f64 x (cos.f64 eps) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 x (cos.f64 eps) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 x (cos.f64 eps) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) (sin.f64 eps)) |
eps |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (fma.f64 x (cos.f64 eps) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) x) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (fma.f64 x (cos.f64 eps) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 x (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/10080 binary64)) #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 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)) (neg.f64 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 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (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 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* 1/120 x) |
(*.f64 x #s(literal 1/120 binary64)) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* -1/5040 (pow x 3)) |
(*.f64 (*.f64 x x) (*.f64 #s(literal -1/5040 binary64) x)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* -1/5040 (pow x 3)) |
(*.f64 (*.f64 x x) (*.f64 #s(literal -1/5040 binary64) x)) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) x) (*.f64 x x)) |
| 7 050× | lower-fma.f32 |
| 7 036× | lower-fma.f64 |
| 5 248× | lower-*.f32 |
| 5 226× | lower-*.f64 |
| 4 432× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 222 |
| 0 | 82 | 204 |
| 1 | 296 | 204 |
| 2 | 2349 | 204 |
| 0 | 9886 | 204 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(*.f64 x (*.f64 x x)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(*.f64 eps #s(literal -1/6 binary64)) |
| Outputs |
|---|
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (pow.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)))))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) |
eps |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
(-.f64 eps #s(literal 0 binary64)) |
(-.f64 eps (/.f64 #s(literal 0 binary64) eps)) |
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps))) |
(fma.f64 eps (/.f64 eps eps) #s(literal 0 binary64)) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64)) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64)) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)) |
(/.f64 (*.f64 eps eps) eps) |
(/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps eps))) |
(/.f64 (-.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps)) |
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) eps))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (*.f64 eps eps)))) |
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(fma.f64 (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) x (*.f64 x #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/5040 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/120 binary64))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728000 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (-.f64 (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64)))) |
(/.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64))) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))) |
(/.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x) (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728000 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (-.f64 (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64))))) (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 x #s(literal 1/120 binary64))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)))) (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/1728000 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))))) (fma.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x #s(literal 1/120 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64)))) (*.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/5040 binary64))))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) |
(*.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) x) |
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))) |
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)) |
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) eps) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps eps)) eps #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal -1/6 binary64) eps) (*.f64 eps eps) #s(literal 0 binary64)) |
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(/.f64 (neg.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (neg.f64 eps)) |
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64)) (*.f64 eps eps)) |
(/.f64 (neg.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (*.f64 eps eps))) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))) (neg.f64 (*.f64 eps eps))) |
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/216 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/216 binary64) #s(literal 0 binary64)) (fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal -1/6 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))))) |
(*.f64 eps #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) eps) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) eps)) |
(*.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 eps (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps eps)) (/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (*.f64 eps eps)) eps) |
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 eps eps)) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) eps))) |
(*.f64 (/.f64 #s(literal -1/6 binary64) eps) (*.f64 eps eps)) |
Compiled 31 531 to 2 507 computations (92% saved)
21 alts after pruning (18 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 038 | 14 | 1 052 |
| Fresh | 1 | 4 | 5 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 042 | 21 | 1 063 |
| Status | Accuracy | Program |
|---|---|---|
| 7.0% | (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) | |
| ✓ | 62.1% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ✓ | 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
| ✓ | 60.8% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
| 55.9% | (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.8% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 99.5% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))) | |
| 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) | |
| ▶ | 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) | |
| ▶ | 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
| 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) | |
| ▶ | 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) | |
| 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
Compiled 821 to 481 computations (41.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) | |
| cost-diff | 0 | (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) | |
| cost-diff | 0 | (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) | |
| cost-diff | 0 | (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| cost-diff | 128 | (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) | |
| cost-diff | 384 | (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) | |
| cost-diff | 0 | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) | |
| cost-diff | 0 | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) | |
| cost-diff | 0 | #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) | |
| cost-diff | 192 | (+.f64 eps #s(literal 0 binary64)) | |
| cost-diff | 832 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
| 16 604× | lower-fma.f32 |
| 16 586× | lower-fma.f64 |
| 3 584× | lower-*.f32 |
| 3 546× | lower-*.f64 |
| 3 180× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 678 |
| 0 | 121 | 661 |
| 1 | 239 | 661 |
| 2 | 683 | 658 |
| 3 | 1906 | 626 |
| 4 | 3226 | 626 |
| 5 | 3587 | 626 |
| 6 | 5151 | 626 |
| 7 | 6445 | 626 |
| 8 | 7011 | 626 |
| 0 | 8234 | 591 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
#s(literal 0 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 x eps) |
x |
#s(literal 2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
eps |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
x |
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) |
#s(literal -1/2 binary64) |
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)) |
(*.f64 eps #s(literal 1/12 binary64)) |
#s(literal 1/12 binary64) |
(+.f64 x eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
eps |
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 x #s(literal -1/2 binary64)) |
x |
#s(literal -1/2 binary64) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(cos.f64 x) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) |
#s(literal -1/645120 binary64) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (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 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
eps |
#s(literal 0 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) |
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 x eps) |
x |
#s(literal 2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps)) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)) eps) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))))) |
eps |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)))) |
(fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))) |
x |
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) |
(*.f64 (+.f64 eps x) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) |
(fma.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 eps x) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)) |
(*.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x))) |
(*.f64 eps #s(literal 1/12 binary64)) |
#s(literal 1/12 binary64) |
(+.f64 x eps) |
(+.f64 eps x) |
(*.f64 eps #s(literal -1/2 binary64)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
eps |
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 x #s(literal -1/2 binary64)) |
x |
#s(literal -1/2 binary64) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(cos.f64 x) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) |
#s(literal -1/645120 binary64) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| accuracy | 0.0347690109686748 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) | |
| accuracy | 0.1015625 | (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) | |
| accuracy | 0.00390625 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) | |
| accuracy | 0.01171875 | (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal -1/6 binary64)) | |
| accuracy | 1.3530855079239983 | #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) | |
| accuracy | 0.15234375 | (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal 1/12 binary64)) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal -1/6 binary64)) | |
| accuracy | 0.7815727822122579 | #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 0 | (*.f64 eps eps) | |
| accuracy | 0.00390625 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) | |
| accuracy | 0.15625 | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) | |
| accuracy | 1.4470883276804993 | #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) | |
| accuracy | 0.015625 | (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) | |
| accuracy | 0.0347690109686748 | (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) | |
| accuracy | 0.265625 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
| 83.0ms | 90× | 1 | valid |
| 80.0ms | 158× | 0 | valid |
| 47.0ms | 6× | 5 | exit |
| 1.0ms | 1× | 3 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 466 to 60 computations (87.1% saved)
ival-mult: 103.0ms (61% of total)const: 18.0ms (10.7% of total)ival-add: 18.0ms (10.7% of total)adjust: 13.0ms (7.7% of total)ival-sin: 6.0ms (3.6% of total)ival-cos: 5.0ms (3% of total)ival-div: 3.0ms (1.8% of total)ival-sub: 1.0ms (0.6% of total)exact: 1.0ms (0.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))> |
#<alt (+.f64 eps #s(literal 0 binary64))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))> |
#<alt (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))> |
#<alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))> |
#<alt (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)> |
#<alt (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))> |
#<alt (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64)))> |
#<alt (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))> |
#<alt (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))))> |
#<alt (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))> |
#<alt (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))> |
#<alt #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64)))> |
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))> |
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))> |
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))> |
#<alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))> |
#<alt (*.f64 eps eps)> |
#<alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))> |
#<alt (*.f64 eps #s(literal -1/6 binary64))> |
#<alt (*.f64 eps #s(literal 1/12 binary64))> |
#<alt (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))> |
#<alt (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))> |
| Outputs |
|---|
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/2 x)> |
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))> |
#<alt (+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))> |
#<alt -1/2> |
#<alt (- (* 1/12 (* eps x)) 1/2)> |
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)> |
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (/ x eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 (* eps x))> |
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))> |
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))> |
#<alt (* eps (+ (* 1/12 eps) (* 1/12 x)))> |
#<alt (* 1/3840 eps)> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt -1/48> |
#<alt (- (* 1/3840 (pow eps 2)) 1/48)> |
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)> |
#<alt (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* 1/12 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))> |
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* -1/645120 (pow eps 3))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (* -1/645120 (pow eps 4))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* 1/12 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* -1/645120 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (* -1/645120 (pow eps 4))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* -1/2 eps)> |
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))> |
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))> |
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))> |
#<alt (- (* 1/12 (pow eps 2)) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))> |
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))> |
#<alt (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2)))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* 1/12 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (/ x eps)> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))> |
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))> |
#<alt (* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* 1/12 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (/ x eps)> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))> |
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))> |
#<alt (* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x)))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 64.0ms | x | @ | -inf | ((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48)) |
| 6.0ms | eps | @ | 0 | ((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48)) |
| 4.0ms | eps | @ | -inf | ((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48)) |
| 4.0ms | eps | @ | inf | ((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48)) |
| 3.0ms | x | @ | inf | ((* eps (+ 1/2 (/ x eps))) (+ eps 0) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* -1/6 (* eps eps)) (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (+ -1/2 (* (* eps 1/12) (+ x eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* -1/2 (sin x)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* eps eps) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (* eps -1/6) (* eps 1/12) (* (* eps 1/12) (+ x eps)) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (cos (* (+ (* x 2) eps) 1/2)) (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48)) |
| 1× | egg-herbie |
| 14 778× | lower-fma.f64 |
| 14 778× | lower-fma.f32 |
| 7 318× | lower-*.f64 |
| 7 318× | lower-*.f32 |
| 3 516× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 432 | 6772 |
| 1 | 1343 | 6403 |
| 2 | 3855 | 6383 |
| 0 | 8456 | 5859 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
eps |
eps |
eps |
eps |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/2 x) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2))) |
-1/2 |
(- (* 1/12 (* eps x)) 1/2) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (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 x) |
(+ (cos x) (* -1/2 (* eps (sin 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))))) |
(/ x eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 (* eps x)) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(* 1/3840 eps) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin 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))))) |
-1/48 |
(- (* 1/3840 (pow eps 2)) 1/48) |
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) |
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (pow eps 3)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* 1/12 (* (pow eps 2) x)) |
(* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps)))) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* -1/645120 (pow eps 3)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(* -1/645120 (pow eps 4)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
eps |
eps |
eps |
eps |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1/6 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* 1/12 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x))) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x))) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x))) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps)))) |
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* -1/645120 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(* -1/645120 (pow eps 4)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))) |
(- (* 1/12 (pow eps 2)) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(* -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)) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (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))))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(* 1/12 (pow eps 2)) |
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) |
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) |
(+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) |
(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 |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* 1/12 (* eps (pow x 2))) |
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x)))) |
(* 1/12 (* eps x)) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(/ x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* 1/12 (* eps x)) |
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) |
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) |
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* 1/12 (* eps (pow x 2))) |
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(* 1/12 (* eps x)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(/ x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* 1/12 (* eps x)) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
| Outputs |
|---|
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
eps |
eps |
eps |
eps |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2))) |
(fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2))) |
(fma.f64 eps (fma.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/12 (* eps x)) 1/2) |
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(/ x eps) |
(/.f64 x eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
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(*.f64 eps #s(literal -1/6 binary64)) |
(* -1/6 eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
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(* 1/12 eps) |
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(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) eps)) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) eps)) |
(* eps (+ (* 1/12 eps) (* 1/12 x))) |
(*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) eps)) |
(* 1/3840 eps) |
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(cos x) |
(cos.f64 x) |
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-1/48 |
#s(literal -1/48 binary64) |
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(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) |
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(* eps (+ 1/2 (/ x eps))) |
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(* 1/12 (* (pow eps 2) x)) |
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(* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps)))) |
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(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps)))) |
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(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps)))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 1/12 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal -1/2 binary64) eps)))) |
(* 1/12 (pow eps 2)) |
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(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
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(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
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(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
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(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (*.f64 eps (cos.f64 x))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
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(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (*.f64 eps (cos.f64 x))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(*.f64 eps (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
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(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps))))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
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(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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1/2 |
#s(literal 1/2 binary64) |
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(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1/645120 (pow eps 4)) |
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) |
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(fma.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))) |
(fma.f64 x (fma.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 (*.f64 x #s(literal -1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
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(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))) |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))) |
(fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))) |
(fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) |
(- (* 1/12 (pow eps 2)) 1/2) |
(fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(+ 1 (* -1/6 (pow eps 2))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/10080 binary64)) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.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 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))) |
(fma.f64 x (fma.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
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x |
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(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(* x (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* 1/12 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal 1/12 binary64)))) |
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) (fma.f64 (*.f64 eps eps) #s(literal -1/12 binary64) #s(literal 1/2 binary64))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal 1/12 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) (fma.f64 (*.f64 eps eps) #s(literal -1/12 binary64) #s(literal 1/2 binary64))) x))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/ x eps) |
(/.f64 x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(* -1 (* x (+ (* -1/12 eps) (* -1/12 (/ (pow eps 2) x))))) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| 6 596× | lower-*.f32 |
| 6 558× | lower-*.f64 |
| 5 984× | lower-fma.f32 |
| 5 966× | lower-fma.f64 |
| 3 878× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 521 |
| 0 | 121 | 509 |
| 1 | 445 | 506 |
| 2 | 4041 | 506 |
| 0 | 10242 | 489 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(+.f64 eps #s(literal 0 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
(*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) |
#s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(*.f64 eps eps) |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(*.f64 eps #s(literal -1/6 binary64)) |
(*.f64 eps #s(literal 1/12 binary64)) |
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps)) |
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
| Outputs |
|---|
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64))) |
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(+.f64 (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) |
(fma.f64 eps (/.f64 x eps) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 x #s(literal 1 binary64))) |
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 x eps) eps (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(fma.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(fma.f64 (*.f64 eps x) (/.f64 #s(literal 1 binary64) eps) (*.f64 eps #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (*.f64 eps eps))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps)) (*.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) eps)) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps eps))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (*.f64 eps eps)) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps)) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))) (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64)))) |
(/.f64 (*.f64 eps (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(/.f64 (*.f64 eps (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 eps eps)) eps) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) eps) |
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) eps) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) eps) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps eps)) (*.f64 eps (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 eps x))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 x (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (/.f64 eps x) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 (/.f64 eps x) (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (/.f64 eps x) eps) (*.f64 eps (*.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (*.f64 eps (*.f64 (/.f64 eps x) eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (neg.f64 x) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (neg.f64 (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (neg.f64 eps) eps) (*.f64 eps (*.f64 (neg.f64 x) (*.f64 eps eps)))) (*.f64 eps (*.f64 (neg.f64 eps) eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) x))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 eps eps) (/.f64 eps x)) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1 binary64)))) (*.f64 eps (*.f64 (*.f64 eps eps) (/.f64 eps x)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (neg.f64 x)))) (*.f64 eps (neg.f64 (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps eps) x))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (neg.f64 eps)) (*.f64 eps (*.f64 (*.f64 eps eps) (neg.f64 x)))) (*.f64 eps (*.f64 eps (neg.f64 eps)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 eps (*.f64 (neg.f64 x) eps))) (*.f64 eps (neg.f64 eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps (/.f64 eps x)) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 eps (*.f64 eps (/.f64 eps x)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps (*.f64 eps #s(literal 1 binary64)))) (*.f64 eps (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 x (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (/.f64 x eps) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 (/.f64 x eps) (*.f64 eps eps)))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 eps) (*.f64 eps (*.f64 eps (neg.f64 x)))) (*.f64 eps (neg.f64 eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (/.f64 eps x) (*.f64 eps (*.f64 #s(literal 1 binary64) eps))) (*.f64 eps (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 x eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps (*.f64 eps (*.f64 (*.f64 eps eps) (/.f64 x eps)))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 eps x) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) eps (*.f64 (*.f64 eps eps) (*.f64 eps x))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 eps x) (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (*.f64 (/.f64 eps x) (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 eps x) eps) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 (/.f64 eps x) eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 (neg.f64 x) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (neg.f64 eps) eps) (*.f64 (*.f64 eps eps) (*.f64 (neg.f64 x) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 (neg.f64 eps) eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) x))) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (/.f64 eps x)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (/.f64 eps x)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (neg.f64 x)))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) x))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (neg.f64 eps)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (neg.f64 x)))) (*.f64 (*.f64 eps eps) (*.f64 eps (neg.f64 eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (neg.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 (neg.f64 x) eps))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps (/.f64 eps x)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (*.f64 eps eps) (*.f64 eps (/.f64 eps x)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 eps x) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1 binary64)))) (*.f64 (*.f64 eps eps) (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (/.f64 x eps) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) eps (*.f64 (*.f64 eps eps) (*.f64 (/.f64 x eps) (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (neg.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 eps (neg.f64 x)))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 eps x) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 eps eps) (/.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 x eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (/.f64 x eps)))) (*.f64 eps (*.f64 eps eps))) |
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(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) eps (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) eps (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) eps (*.f64 eps (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps eps)))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) eps (*.f64 eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) eps (*.f64 eps (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps eps)))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (*.f64 eps eps) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) eps (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps eps)))) (*.f64 eps (*.f64 eps eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps (*.f64 eps eps)) eps)) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) eps) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))) |
(+.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/48 binary64)) |
(-.f64 (/.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))) (/.f64 #s(literal 1/2304 binary64) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))) |
(fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) |
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(fma.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) eps #s(literal -1/48 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)) (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)) (+.f64 #s(literal 1/2304 binary64) (-.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))))) |
(/.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64))) (neg.f64 (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) (neg.f64 (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))) |
(/.f64 (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))))))) (-.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) |
(pow.f64 (/.f64 (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)) (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) #s(literal -1/110592 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal 1/2304 binary64)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))))) |
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) (*.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal 1/48 binary64)))) |
Compiled 46 573 to 4 548 computations (90.2% saved)
25 alts after pruning (22 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 506 | 14 | 1 520 |
| Fresh | 5 | 8 | 13 |
| Picked | 4 | 1 | 5 |
| Done | 1 | 2 | 3 |
| Total | 1 516 | 25 | 1 541 |
| Status | Accuracy | Program |
|---|---|---|
| 7.0% | (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) | |
| ✓ | 62.1% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ✓ | 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) | |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) | |
| ▶ | 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.5% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| 55.3% | #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) | |
| 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))) | |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) | |
| 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| ▶ | 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 98.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) | |
| ✓ | 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
| 97.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) | |
| ▶ | 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
Compiled 999 to 578 computations (42.1% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| cost-diff | 0 | (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) | |
| cost-diff | 0 | #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) | |
| cost-diff | 0 | #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) | |
| cost-diff | 0 | (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) | |
| cost-diff | 832 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
| 6 930× | lower-fma.f32 |
| 6 916× | lower-fma.f64 |
| 4 320× | lower-*.f32 |
| 4 282× | lower-*.f64 |
| 2 626× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 736 |
| 0 | 120 | 723 |
| 1 | 230 | 720 |
| 2 | 585 | 709 |
| 3 | 1306 | 688 |
| 4 | 1776 | 688 |
| 5 | 2374 | 688 |
| 6 | 4451 | 688 |
| 7 | 5536 | 688 |
| 8 | 6199 | 688 |
| 9 | 7451 | 688 |
| 0 | 8259 | 645 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 x eps) |
x |
#s(literal 2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))) |
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
eps |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
x |
(fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) |
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) |
(*.f64 x #s(literal 1/12 binary64)) |
#s(literal 1/12 binary64) |
#s(literal -1/2 binary64) |
(*.f64 eps #s(literal -1/2 binary64)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) |
(*.f64 eps #s(literal 1/3840 binary64)) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x))) |
#s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
#s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 x eps) |
x |
#s(literal 2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(*.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
eps |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
x |
(fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) |
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) |
(*.f64 x #s(literal 1/12 binary64)) |
#s(literal 1/12 binary64) |
#s(literal -1/2 binary64) |
(*.f64 eps #s(literal -1/2 binary64)) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 eps #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.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) |
eps |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) |
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) |
(*.f64 eps #s(literal 1/3840 binary64)) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| accuracy | 0.0347690109686748 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) | |
| accuracy | 0.09375 | (*.f64 eps #s(literal 1/3840 binary64)) | |
| accuracy | 0.09405278396361128 | #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) eps) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) | |
| accuracy | 0.0347690109686748 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) | |
| accuracy | 0.13604784108788315 | #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0.15592698211911837 | #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) | |
| accuracy | 0.33984375 | (*.f64 x #s(literal 1/12 binary64)) | |
| accuracy | 0.36328125 | (*.f64 eps #s(literal -1/6 binary64)) | |
| accuracy | 0.7815727822122579 | #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 0.0859375 | (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) | |
| accuracy | 0.15625 | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) | |
| accuracy | 1.4470883276804993 | #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))) | |
| accuracy | 59.388952759127505 | #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) | |
| accuracy | 0.015625 | (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) | |
| accuracy | 0.0347690109686748 | (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) | |
| accuracy | 0.265625 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
| 83.0ms | 158× | 0 | valid |
| 78.0ms | 90× | 1 | valid |
| 38.0ms | 6× | 5 | exit |
| 1.0ms | 1× | 3 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 441 to 68 computations (84.6% saved)
ival-mult: 100.0ms (60.1% of total)ival-add: 18.0ms (10.8% of total)const: 17.0ms (10.2% of total)adjust: 14.0ms (8.4% of total)ival-sin: 8.0ms (4.8% of total)ival-cos: 4.0ms (2.4% of total)ival-div: 3.0ms (1.8% of total)ival-sub: 2.0ms (1.2% of total)exact: 1.0ms (0.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64))> |
#<alt (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))> |
#<alt (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))> |
#<alt #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))> |
#<alt #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))> |
#<alt (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))> |
#<alt #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))))> |
#<alt (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))> |
#<alt #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))> |
#<alt (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))> |
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))> |
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps))> |
#<alt (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))> |
#<alt (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))> |
#<alt (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))> |
#<alt (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))> |
#<alt (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))> |
#<alt (*.f64 eps #s(literal -1/6 binary64))> |
#<alt (*.f64 x #s(literal 1/12 binary64))> |
#<alt #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (*.f64 #s(literal 1/2 binary64) eps)> |
#<alt #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64)))> |
#<alt (*.f64 eps #s(literal 1/3840 binary64))> |
| Outputs |
|---|
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))> |
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (/ x eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (/ (+ x (* 1/2 eps)) eps)> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt -1/2> |
#<alt (- (* 1/12 (* eps x)) 1/2)> |
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)> |
#<alt (- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2)> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* eps (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* 1/12 (pow x 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))> |
#<alt (* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1/645120 (pow eps 3))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6))> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))> |
#<alt (* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1/645120 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 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))))))))> |
#<alt (+ (* 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))))))))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt 1/2> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (+ 1/2 (/ x eps))> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (- (* 1/12 (pow eps 2)) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x))))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (/ x eps)> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 (* eps x))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (/ x eps)> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 (* eps x))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 26.0ms | eps | @ | -inf | ((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840)) |
| 4.0ms | eps | @ | inf | ((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840)) |
| 3.0ms | eps | @ | 0 | ((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840)) |
| 3.0ms | x | @ | -inf | ((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840)) |
| 3.0ms | x | @ | inf | ((* eps (+ 1/2 (/ x eps))) (* (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* eps 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* eps 1/2)) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/6 (* eps eps))) eps) (* eps (* -1/6 (* eps eps))) (- (sin (+ x eps)) (sin x)) (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (* (+ (* x 2) eps) 1/2) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)) (+ 1/2 (/ x eps)) (* -1/6 (* eps eps)) (* eps -1/6) (* x 1/12) (+ -1/2 (* (* eps 1/12) (+ x eps))) (cos (* (+ (* x 2) eps) 1/2)) (* 1/2 eps) (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (* eps 1/3840)) |
| 1× | egg-herbie |
| 12 802× | lower-fma.f64 |
| 12 802× | lower-fma.f32 |
| 7 180× | lower-*.f64 |
| 7 180× | lower-*.f32 |
| 2 982× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 444 | 6501 |
| 1 | 1396 | 6107 |
| 2 | 4226 | 6095 |
| 0 | 8379 | 5603 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (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)))) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* 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))))))))) |
(* 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)) (* -1/6 (* eps (cos x))))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (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)))) |
(* eps (cos 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)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (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 x) |
(+ (cos x) (* -1/2 (* eps (sin 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))))) |
(/ x eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(/ (+ x (* 1/2 eps)) eps) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
-1/2 |
(- (* 1/12 (* eps x)) 1/2) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(- (* eps (+ (* 1/12 eps) (* 1/12 x))) 1/2) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin 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) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/3840 eps) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* eps (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (pow eps 3)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6)) |
(* (pow eps 2) (- (+ (* 1/12 (pow x 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)) 1/6)) |
(* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6)) |
(* (pow eps 2) (- (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (+ (/ 1 (pow eps 2)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)))) 1/6)) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
(* (pow eps 2) (- (+ 1/12 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* -1/645120 (pow eps 3)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 3) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1/6 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(* -1/6 (pow eps 3)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6)) |
(* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) 1/6)) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6)) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6)) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/12 (pow eps 2)) |
(* (pow eps 2) (+ 1/12 (* 1/12 (/ x eps)))) |
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps)))) |
(* (pow eps 2) (+ 1/12 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* -1/645120 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(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 (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (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)))))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (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))))) |
1/2 |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(+ 1/2 (/ x eps)) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(- (* 1/12 (pow eps 2)) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2) |
(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 |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* 1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x)))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(/ x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 (* eps x)) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* 1/12 (* eps (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(/ x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 (* eps x)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
| Outputs |
|---|
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* -1/6 (pow eps 3)) |
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
(* -1/6 (pow eps 3)) |
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
(* -1/6 (pow eps 3)) |
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
(* -1/6 (pow eps 3)) |
(*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/6 binary64)) (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 1/2 (* eps (cos x))) |
(*.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
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(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.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 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
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(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1/6 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) x) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (sin.f64 eps)) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) x) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) |
(+ 1 (* -1/6 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(+ 1 (* -1/6 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(fma.f64 x (*.f64 eps #s(literal -1/2 binary64)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))))) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.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 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1/6 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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))))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.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 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
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(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)) (neg.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
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(fma.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
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(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
1/2 |
#s(literal 1/2 binary64) |
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(*.f64 x #s(literal 1/12 binary64)) |
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(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
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(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) |
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(fma.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps) #s(literal -1/2 binary64)) |
(cos (* 1/2 eps)) |
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x |
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
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(- (sin (+ eps x)) (sin x)) |
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(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(* 1/12 (* eps (pow x 3))) |
(*.f64 eps (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 x x)))) |
(* (pow x 3) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x (fma.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))) #s(literal -1/2 binary64))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 eps) (+ (* 1/12 (/ (pow eps 2) x)) (/ 1 (pow x 3)))))) (* 1/2 (/ 1 x)))) |
(*.f64 (*.f64 x x) (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x))) (fma.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) #s(literal -1/2 binary64))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 (/.f64 eps x) (*.f64 x #s(literal 1/2 binary64)) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 (/.f64 eps x) (*.f64 x #s(literal 1/2 binary64)) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 (/.f64 eps x) (*.f64 x #s(literal 1/2 binary64)) x) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/ x eps) |
(/.f64 x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
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(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
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(* 1/12 x) |
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(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 (* eps x)) |
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(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
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(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
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(* x (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
x |
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(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) |
(* 1/12 (* eps (pow x 3))) |
(*.f64 eps (*.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps)))) |
(neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 eps #s(literal -1/12 binary64)) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) x)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* -1/12 eps)))) |
(neg.f64 (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 eps #s(literal -1/12 binary64) (/.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) x) (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(/ x eps) |
(/.f64 x eps) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x)))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* -1/12 eps)))) |
(fma.f64 x (*.f64 #s(literal 1/12 binary64) (fma.f64 eps (/.f64 eps x) eps)) #s(literal -1/2 binary64)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| 6 340× | lower-*.f32 |
| 6 302× | lower-*.f64 |
| 5 716× | lower-fma.f32 |
| 5 702× | lower-fma.f64 |
| 3 654× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 571 |
| 0 | 120 | 559 |
| 1 | 434 | 545 |
| 2 | 3865 | 545 |
| 0 | 9786 | 524 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))) |
#s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))))) |
#s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 eps #s(literal -1/6 binary64)) |
(*.f64 x #s(literal 1/12 binary64)) |
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) |
(*.f64 eps #s(literal 1/3840 binary64)) |
| Outputs |
|---|
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x #s(literal 1 binary64))) |
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(+.f64 (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) |
(fma.f64 eps (/.f64 x eps) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(fma.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 x #s(literal 1 binary64))) |
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 x eps) eps (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) #s(literal 0 binary64))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) eps (*.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
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(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 #s(literal 2 binary64) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
#s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) |
(cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))))) |
(+.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) |
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (/.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1 binary64) (/.f64 x eps) #s(literal 1/2 binary64)) |
(fma.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 eps)) #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) x #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 x (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 (/.f64 x (*.f64 eps eps)) eps #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))))) |
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) eps)))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1/4 binary64)) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(pow.f64 (/.f64 (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x eps) (-.f64 (/.f64 x eps) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(+.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) eps (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64)) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64))) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64)))) |
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) eps) |
(/.f64 (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
(*.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) eps) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1 binary64))) |
(*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) |
(+.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal -1/6 binary64))) |
(fma.f64 eps #s(literal -1/6 binary64) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) |
(/.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps) |
(*.f64 eps #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) eps) |
(*.f64 x #s(literal 1/12 binary64)) |
(*.f64 #s(literal 1/12 binary64) x) |
#s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) eps) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) |
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/3840 binary64))) |
(+.f64 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 0 binary64)) |
(fma.f64 eps #s(literal 1/3840 binary64) #s(literal 0 binary64)) |
(fma.f64 #s(literal 1/3840 binary64) eps #s(literal 0 binary64)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) |
(/.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) eps) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/3840 binary64)) (*.f64 eps eps)) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(*.f64 #s(literal 1/3840 binary64) eps) |
Compiled 38 535 to 2 868 computations (92.6% saved)
25 alts after pruning (22 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 164 | 8 | 1 172 |
| Fresh | 3 | 14 | 17 |
| Picked | 3 | 2 | 5 |
| Done | 2 | 1 | 3 |
| Total | 1 172 | 25 | 1 197 |
| Status | Accuracy | Program |
|---|---|---|
| 7.0% | (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) | |
| ✓ | 62.1% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) | |
| ✓ | 99.9% | (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) | |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) | |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) | |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 99.5% | (*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) | |
| 55.3% | #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) | |
| 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))) | |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) | |
| 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) | |
| 98.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 98.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) | |
| 98.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) | |
| 98.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) | |
| 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) | |
| 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) | |
| 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) | |
| ✓ | 5.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
Compiled 1 379 to 490 computations (64.5% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
3 calls:
| 18.0ms | x |
| 13.0ms | eps |
| 12.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
3 calls:
| 12.0ms | x |
| 11.0ms | eps |
| 11.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
3 calls:
| 16.0ms | x |
| 12.0ms | eps |
| 10.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
3 calls:
| 10.0ms | eps |
| 10.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 9.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (*.f64 eps eps)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
3 calls:
| 11.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 10.0ms | x |
| 9.0ms | 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 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(approx (+ (* eps (* eps (+ (* (* eps eps) -1/645120) 1/3840))) -1/48) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
3 calls:
| 13.0ms | eps |
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
| 99.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 eps #s(approx (* -1/2 (sin x)) (*.f64 x #s(literal -1/2 binary64))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
3 calls:
| 9.0ms | x |
| 9.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
3 calls:
| 8.0ms | x |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (+.f64 x eps))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x (fma.f64 (*.f64 x #s(literal 1/12 binary64)) (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
3 calls:
| 12.0ms | eps |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
3 calls:
| 5.0ms | eps |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
3 calls:
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
3 calls:
| 4.0ms | eps |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (+.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 eps #s(literal -1/6 binary64) (*.f64 x #s(literal -1/2 binary64))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x #s(approx (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2)) (*.f64 x #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
3 calls:
| 6.0ms | x |
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/6 binary64))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.1% | 1 | x |
| 5.1% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.1% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 74× | *-commutative_binary64 |
| 6× | +-commutative_binary64 |
| 2× | +-rgt-identity_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 144 | 577 |
| 1 | 188 | 577 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps #s(approx (* eps (+ (* (* eps eps) -1/645120) 1/3840)) (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 #s(approx (* (+ (* x 2) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* (+ eps 0) 1/2)) (*.f64 eps #s(literal 1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (cos.f64 x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) (fma.f64 eps (*.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) x) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) (fma.f64 x (fma.f64 x #s(approx (+ -1/2 (* (* eps 1/12) (+ x eps))) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps #s(approx (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x))) #s(approx (+ (* x (+ (* x (+ -1/2 (* (* eps 1/12) (+ x eps)))) (* eps -1/2))) (+ (* eps (* eps -1/6)) 1)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* eps (+ (* eps (* -1/2 (sin x))) (* (+ (* eps (* eps -1/6)) 1) (cos x)))) #s(approx (+ (* eps (* -1/6 (* eps eps))) eps) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))) |
| 16 678× | lower-fma.f64 |
| 16 678× | lower-fma.f32 |
| 15 108× | lower-fma.f64 |
| 15 108× | lower-fma.f32 |
| 14 778× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2829 | 489 |
| 4 | 6198 | 489 |
| 0 | 8141 | 458 |
| 0 | 432 | 6772 |
| 1 | 1343 | 6403 |
| 2 | 3855 | 6383 |
| 0 | 8456 | 5859 |
| 0 | 379 | 3701 |
| 1 | 1190 | 3521 |
| 2 | 3339 | 3483 |
| 0 | 8299 | 3200 |
| 0 | 444 | 6501 |
| 1 | 1396 | 6107 |
| 2 | 4226 | 6095 |
| 0 | 8379 | 5603 |
| 0 | 76 | 521 |
| 0 | 121 | 509 |
| 1 | 445 | 506 |
| 2 | 4041 | 506 |
| 0 | 10242 | 489 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 828 to 436 computations (47.3% saved)
Compiled 660 to 236 computations (64.2% saved)
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