
Time bar (total: 15.1s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 74.7% | 0% | 0% | 0% | 3 |
| 0% | 0% | 25.3% | 74.7% | 0% | 0% | 0% | 4 |
| 0% | 0% | 19% | 81% | 0% | 0% | 0% | 5 |
| 0% | 0% | 15.8% | 84.2% | 0% | 0% | 0% | 6 |
| 0% | 0% | 11.1% | 88.9% | 0% | 0% | 0% | 7 |
| 0% | 0% | 8.7% | 91.3% | 0% | 0% | 0% | 8 |
| 0% | 0% | 5.9% | 94.1% | 0% | 0% | 0% | 9 |
| 0% | 0% | 4.5% | 95.5% | 0% | 0% | 0% | 10 |
| 0% | 0% | 3.1% | 96.9% | 0% | 0% | 0% | 11 |
| 0% | 0% | 2.7% | 97.3% | 0% | 0% | 0% | 12 |
Compiled 28 to 18 computations (35.7% saved)
ival-sin: 8.0ms (22.8% of total)...c/correct-round.rkt:119:19: 7.0ms (20% of total)ival-<=: 4.0ms (11.4% of total)ival-add: 3.0ms (8.6% of total)ival-mult: 3.0ms (8.6% of total)ival-fabs: 3.0ms (8.6% of total)ival-<: 3.0ms (8.6% of total)ival-sub: 2.0ms (5.7% of total)ival-and: 1.0ms (2.9% of total)const: 1.0ms (2.9% of total)backward-pass: 0.0ms (0% of total)| 4.2s | 26557× | 0 | precondition |
| 1.1s | 4475× | 1 | valid |
| 535.0ms | 3781× | 0 | valid |
ival-sin: 1.2s (27.1% of total)...c/correct-round.rkt:119:19: 934.0ms (20.5% of total)ival-add: 383.0ms (8.4% of total)ival-<=: 368.0ms (8.1% of total)ival-<: 359.0ms (7.9% of total)ival-mult: 355.0ms (7.8% of total)ival-sub: 340.0ms (7.4% of total)ival-fabs: 304.0ms (6.7% of total)ival-and: 133.0ms (2.9% of total)backward-pass: 104.0ms (2.3% of total)const: 48.0ms (1.1% of total)| 2× | egg-herbie |
| 376× | fnmadd-define |
| 344× | fnmsub-define |
| 344× | fmsub-define |
| 320× | sum3-define |
| 308× | fmm-def |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 46 |
| 1 | 43 | 42 |
| 2 | 94 | 42 |
| 3 | 198 | 42 |
| 4 | 507 | 42 |
| 5 | 917 | 42 |
| 6 | 1285 | 42 |
| 7 | 1548 | 42 |
| 8 | 1684 | 42 |
| 9 | 1711 | 42 |
| 0 | 6 | 7 |
| 1 | 9 | 7 |
| 2 | 14 | 7 |
| 3 | 21 | 7 |
| 4 | 31 | 7 |
| 5 | 63 | 7 |
| 6 | 122 | 7 |
| 7 | 210 | 7 |
| 8 | 295 | 7 |
| 9 | 401 | 7 |
| 10 | 479 | 7 |
| 11 | 485 | 7 |
| 0 | 485 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(- (sin (+ (neg x) eps)) (sin (neg x))) |
(- (sin (+ x (neg eps))) (sin x)) |
(neg (- (sin (+ (neg x) eps)) (sin (neg x)))) |
(neg (- (sin (+ x (neg eps))) (sin x))) |
(- (sin (+ eps x)) (sin eps)) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(- (sin (+ (neg x) eps)) (sin (neg x))) |
(+ (sin x) (sin (- eps x))) |
(- (sin (+ x (neg eps))) (sin x)) |
(- (sin (- x eps)) (sin x)) |
(neg (- (sin (+ (neg x) eps)) (sin (neg x)))) |
(- (sin (- x eps)) (sin x)) |
(neg (- (sin (+ x (neg eps))) (sin x))) |
(+ (sin x) (sin (- eps x))) |
(- (sin (+ eps x)) (sin eps)) |
(- (sin (+ x eps)) (sin eps)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 226 | 3 | (-2.3745816446511557e-107 2.300282434976019e-109) | 3 | (-1.4921680009134305e-267 2.651260580027058e-269) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | eps |
| 49.0ms | 292× | 1 | valid |
| 17.0ms | 216× | 0 | valid |
| 1.0ms | 4× | 2 | valid |
Compiled 51 to 20 computations (60.8% saved)
ival-sin: 14.0ms (46.3% of total)ival-add: 7.0ms (23.1% of total)backward-pass: 5.0ms (16.5% of total)ival-sub: 4.0ms (13.2% of total)const: 0.0ms (0% of total)Compiled 9 to 6 computations (33.3% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 61.5% | (-.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)) |
| 124× | fnmadd-define |
| 122× | sum3-define |
| 80× | fma-lowering-fma.f32 |
| 80× | fnmsub-define |
| 80× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 9 | 18 |
| 2 | 14 | 18 |
| 3 | 21 | 18 |
| 4 | 31 | 18 |
| 5 | 63 | 18 |
| 6 | 122 | 18 |
| 7 | 210 | 18 |
| 8 | 295 | 18 |
| 9 | 401 | 18 |
| 10 | 479 | 18 |
| 11 | 485 | 18 |
| 0 | 485 | 18 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(sin x) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (+ x eps)) |
(sin.f64 (+.f64 x eps)) |
(+ x eps) |
(+.f64 x eps) |
x |
eps |
(sin x) |
(sin.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x eps) |
| ✓ | accuracy | 100.0% | (sin.f64 x) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 61.7% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 29.0ms | 146× | 1 | valid |
| 7.0ms | 108× | 0 | valid |
| 0.0ms | 2× | 2 | valid |
Compiled 21 to 7 computations (66.7% saved)
ival-sub: 11.0ms (47.8% of total)ival-sin: 6.0ms (26.1% of total)ival-add: 3.0ms (13% of total)backward-pass: 2.0ms (8.7% of total)const: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- (sin (+ x eps)) (sin x))> |
#<alt (sin (+ x eps))> |
#<alt (+ x eps)> |
#<alt (sin x)> |
| Outputs |
|---|
#<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 x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps 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 (* 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 (+ 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 (* -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) (* 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps 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 x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x 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 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 x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | eps | @ | inf | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | eps | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | inf | (+ x eps) |
| 0.0ms | x | @ | -inf | (- (sin (+ x eps)) (sin x)) |
| 1× | batch-egg-rewrite |
| 2788× | *-lowering-*.f32 |
| 2788× | *-lowering-*.f64 |
| 2132× | /-lowering-/.f32 |
| 2132× | /-lowering-/.f64 |
| 2068× | fma-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 402 | 16 |
| 3 | 5232 | 16 |
| 0 | 8309 | 16 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(sin (+ x eps)) |
(+ x eps) |
(sin x) |
| Outputs |
|---|
(+.f64 (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.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)) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (*.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 (+.f64 (*.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 #s(literal 2 binary64))))) (+.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 (-.f64 #s(literal 0 binary64) (sin.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 (+.f64 (*.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 (+.f64 (*.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 #s(literal 2 binary64))))) (+.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 #s(literal 2 binary64))))) (+.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 (+.f64 (*.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 (+.f64 (*.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 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.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 (+.f64 (*.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 #s(literal 2 binary64))))) (+.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 (+.f64 (*.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 (+.f64 (*.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 (*.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) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (-.f64 #s(literal 0 binary64) (sin.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))) (-.f64 #s(literal 0 binary64) (sin.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 (+.f64 (*.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 (+.f64 (*.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)))))))) |
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(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #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)))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (*.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))))))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #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 (+.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 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(*.f64 (/.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) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (+.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 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps)))) |
(sin.f64 (+.f64 x eps)) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(fma.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (neg.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.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 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) |
(/.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 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (sin.f64 x) (*.f64 (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))) (+.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) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) |
(/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) |
(/.f64 (neg.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)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))) (neg.f64 (sin.f64 (-.f64 x eps)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))) |
(*.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) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))) |
(*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) |
(+.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 x) (*.f64 eps eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(neg.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(neg.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 x eps))) |
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) |
(/.f64 (+.f64 (*.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 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #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 eps eps) (*.f64 x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x)) |
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (+.f64 (*.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 (+.f64 (*.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 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) |
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1 binary64)) (-.f64 x eps)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 x x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (/.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 (*.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)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (*.f64 (+.f64 (*.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) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))) |
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #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 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) |
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x))))) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps)))) |
(sin.f64 x) |
| 1× | egg-herbie |
| 3796× | *-lowering-*.f32 |
| 3796× | *-lowering-*.f64 |
| 2064× | +-lowering-+.f64 |
| 2064× | +-lowering-+.f32 |
| 1456× | fnmadd-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 488 |
| 1 | 327 | 465 |
| 2 | 963 | 459 |
| 3 | 3572 | 459 |
| 0 | 8267 | 459 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps 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 (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 (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (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 eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
| Outputs |
|---|
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(-.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.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 (* -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)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.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 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps 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 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
(- (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 (- 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 eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (*.f64 x (cos.f64 eps)) (*.f64 (+.f64 (*.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)))))))) |
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.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)) |
(sin (+ eps 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)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 (+.f64 (*.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)))))))) |
(+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(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)) |
(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 |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64))))))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
Compiled 7060 to 730 computations (89.7% saved)
12 alts after pruning (11 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 250 | 11 | 261 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 250 | 12 | 262 |
| Status | Accuracy | Program |
|---|---|---|
| 61.7% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) | |
| 36.4% | (/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) | |
| ▶ | 36.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| 61.7% | (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| ▶ | 60.1% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.6% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| ▶ | 99.7% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| 99.4% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| ▶ | 99.3% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 98.6% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 96.7% | (sin.f64 eps) |
Compiled 369 to 218 computations (40.9% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 (-.f64 x eps)) |
| ✓ | cost-diff | 13184 | (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))) |
| ✓ | cost-diff | 13440 | (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) |
| ✓ | cost-diff | 13440 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 128 | (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 128 | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 128 | (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 128 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| 1676× | fma-lowering-fma.f32 |
| 1676× | fma-lowering-fma.f64 |
| 1668× | sum5-define |
| 1650× | sum3-define |
| 1386× | fmm-def |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 216 |
| 1 | 85 | 205 |
| 2 | 242 | 184 |
| 3 | 802 | 182 |
| 4 | 1506 | 182 |
| 5 | 3684 | 182 |
| 6 | 7083 | 182 |
| 0 | 8102 | 182 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(sin (/ (+ eps 0) 2)) |
(/ (+ eps 0) 2) |
(+ eps 0) |
eps |
0 |
2 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
(sin eps) |
eps |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(* x (+ 1 (* x (* x -1/6)))) |
(+ 1 (* x (* x -1/6))) |
1 |
(* x (* x -1/6)) |
(* x -1/6) |
-1/6 |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
eps |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(cos x) |
x |
(* -1/2 (* eps (sin x))) |
-1/2 |
(* eps (sin x)) |
(sin x) |
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x)) |
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) |
1 |
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))) |
(sin (- x eps)) |
(- x eps) |
x |
eps |
(* (sin (+ x eps)) (sin (- x eps))) |
(sin (+ x eps)) |
(+ x eps) |
(sin x) |
| Outputs |
|---|
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) |
(sin (/ (+ eps 0) 2)) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(/ (+ eps 0) 2) |
(/.f64 eps #s(literal 2 binary64)) |
(+ eps 0) |
eps |
eps |
0 |
#s(literal 0 binary64) |
2 |
#s(literal 2 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) |
(/ (+ eps (* x 2)) 2) |
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) |
(+ eps (* x 2)) |
(+.f64 eps (*.f64 #s(literal 2 binary64) x)) |
(* x 2) |
(*.f64 #s(literal 2 binary64) x) |
x |
(sin eps) |
(sin.f64 eps) |
eps |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64)))))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(* x (+ 1 (* x (* x -1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(+ 1 (* x (* x -1/6))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) |
1 |
#s(literal 1 binary64) |
(* x (* x -1/6)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* x -1/6) |
(*.f64 x #s(literal -1/6 binary64)) |
-1/6 |
#s(literal -1/6 binary64) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))) |
eps |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))) |
(cos x) |
(cos.f64 x) |
x |
(* -1/2 (* eps (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) |
(sin.f64 (+.f64 eps x)) |
1 |
#s(literal 1 binary64) |
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(- x eps) |
(-.f64 x eps) |
x |
eps |
(* (sin (+ x eps)) (sin (- x eps))) |
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
(sin x) |
(sin.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.8% | (sin.f64 (-.f64 x eps)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) |
| ✓ | accuracy | 61.7% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| ✓ | accuracy | 57.5% | (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| ✓ | accuracy | 100.0% | (*.f64 eps (sin.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
| ✓ | accuracy | 100.0% | (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
| ✓ | accuracy | 99.5% | (*.f64 x #s(literal -1/6 binary64)) |
| ✓ | accuracy | 62.6% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | accuracy | 100.0% | (sin.f64 eps) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| 145.0ms | 147× | 1 | valid |
| 39.0ms | 105× | 0 | valid |
| 5.0ms | 4× | 2 | valid |
Compiled 242 to 37 computations (84.7% saved)
ival-mult: 40.0ms (35.8% of total)ival-sin: 15.0ms (13.4% of total)ival-div: 13.0ms (11.6% of total)backward-pass: 11.0ms (9.8% of total)ival-add: 11.0ms (9.8% of total)ival-cos: 7.0ms (6.3% of total)...c/correct-round.rkt:119:19: 7.0ms (6.3% of total)ival-sub: 6.0ms (5.4% of total)const: 1.0ms (0.9% of total)| Inputs |
|---|
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (sin (/ (+ eps 0) 2))> |
#<alt (/ (+ eps 0) 2)> |
#<alt (sin eps)> |
#<alt (- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))> |
#<alt (sin (+ x eps))> |
#<alt (+ x eps)> |
#<alt (* x (+ 1 (* x (* x -1/6))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (cos x)> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x))> |
#<alt (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))))> |
#<alt (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))> |
#<alt (sin (- x eps))> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
#<alt (* x 2)> |
#<alt (* x -1/6)> |
#<alt (* x (* x -1/6))> |
#<alt (* eps (sin x))> |
| Outputs |
|---|
#<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 (* 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 (* 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 (* 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 (* 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 (* 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 (* 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 (* (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 (- (* 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 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 (* 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)))) (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 (* 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 (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 (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<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 (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin 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 (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))> |
#<alt (- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps 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 x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x 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 x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* -1/6 (pow x 3))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* -1/6 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))> |
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))> |
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin 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 (- (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 (* -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 (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 (+ 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 (* -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) (* 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (/ 1 (sin eps))> |
#<alt (+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin x))> |
#<alt (+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))> |
#<alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))> |
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (sin (neg eps))> |
#<alt (+ (sin (neg eps)) (* x (cos (neg eps))))> |
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps)))))))> |
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps)))))))))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (neg (+ eps (* -1 x))))> |
#<alt (sin (neg (+ eps (* -1 x))))> |
#<alt (sin (neg (+ eps (* -1 x))))> |
#<alt (sin (neg (+ eps (* -1 x))))> |
#<alt (sin x)> |
#<alt (+ (sin x) (* -1 (* eps (cos x))))> |
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x))))))))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (- x eps))> |
#<alt (sin (+ x (* -1 eps)))> |
#<alt (sin (+ x (* -1 eps)))> |
#<alt (sin (+ x (* -1 eps)))> |
#<alt (sin (+ x (* -1 eps)))> |
#<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 (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 (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 (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 (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 (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 (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps x)> |
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))> |
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))> |
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | x | @ | 0 | (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))) |
| 3.0ms | x | @ | inf | (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
| 1.0ms | x | @ | -inf | (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1.0ms | x | @ | inf | (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1.0ms | eps | @ | 0 | (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1× | batch-egg-rewrite |
| 5990× | *-lowering-*.f32 |
| 5990× | *-lowering-*.f64 |
| 3264× | +-lowering-+.f64 |
| 3264× | +-lowering-+.f32 |
| 2992× | /-lowering-/.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 169 |
| 1 | 218 | 158 |
| 2 | 2224 | 132 |
| 0 | 11117 | 132 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(sin (/ (+ eps 0) 2)) |
(/ (+ eps 0) 2) |
(sin eps) |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(sin (+ x eps)) |
(+ x eps) |
(* x (+ 1 (* x (* x -1/6)))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(cos x) |
(* -1/2 (* eps (sin x))) |
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x)) |
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) |
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))) |
(sin (- x eps)) |
(cos (/ (+ eps (* x 2)) 2)) |
(* x 2) |
(* x -1/6) |
(* x (* x -1/6)) |
(* eps (sin x)) |
| Outputs |
|---|
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))))) |
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -2 binary64)) |
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64)) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 1/2 binary64)) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) eps)) #s(literal -1 binary64))) |
(neg.f64 (/.f64 eps #s(literal -2 binary64))) |
(/.f64 eps #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) eps))) |
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 2 binary64) (*.f64 eps eps))) |
(/.f64 (*.f64 eps eps) (*.f64 #s(literal 2 binary64) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(pow.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 eps #s(literal 2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) eps)) |
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
(-.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps)))) |
(sin.f64 eps) |
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) x))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 eps x))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
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(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (+.f64 eps x)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (+.f64 eps x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps)))))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) |
(+.f64 (sin.f64 (-.f64 x eps)) (+.f64 (*.f64 (sin.f64 (-.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(+.f64 (sin.f64 (-.f64 x eps)) (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 (-.f64 #s(literal 0 binary64) eps)))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(+.f64 (*.f64 (sin.f64 (-.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(-.f64 (*.f64 (sin.f64 (-.f64 x eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (-.f64 x eps)) #s(literal 0 binary64))) |
(-.f64 (*.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 eps x))))) (cos.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 eps x)))))) (*.f64 (cos.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 eps x))))) (sin.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 eps x))))))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (+.f64 eps x))) (cos.f64 (/.f64 (*.f64 eps eps) (+.f64 eps x)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (+.f64 eps x))) (sin.f64 (/.f64 (*.f64 eps eps) (+.f64 eps x))))) |
(sin.f64 (-.f64 x eps)) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 (-.f64 #s(literal 0 binary64) eps)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (neg.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 eps) (cos.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (sin.f64 (+.f64 eps x))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))) |
(*.f64 #s(literal 2 binary64) x) |
(*.f64 x #s(literal 2 binary64)) |
(*.f64 x #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) x) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x #s(literal -1/6 binary64)) x) |
(*.f64 (*.f64 x (*.f64 x #s(literal -1/6 binary64))) #s(literal 1 binary64)) |
(*.f64 (*.f64 x x) #s(literal -1/6 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/6 binary64))) x) |
(+.f64 (*.f64 eps (sin.f64 x)) (*.f64 (sin.f64 x) #s(literal 0 binary64))) |
(+.f64 (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 eps (sin.f64 x))) |
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 eps (sin.f64 x))) |
(fma.f64 eps (sin.f64 x) (*.f64 (sin.f64 x) #s(literal 0 binary64))) |
(fma.f64 eps (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 #s(literal 0 binary64) (sin.f64 x) (*.f64 eps (sin.f64 x))) |
(fma.f64 (sin.f64 x) eps (*.f64 (sin.f64 x) #s(literal 0 binary64))) |
(fma.f64 (sin.f64 x) eps (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 eps (sin.f64 x))) |
(/.f64 (*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) eps) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (sin.f64 x)) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps) |
(*.f64 eps (sin.f64 x)) |
(*.f64 (sin.f64 x) eps) |
| 1× | egg-herbie |
| 4902× | *-lowering-*.f32 |
| 4902× | *-lowering-*.f64 |
| 1704× | +-lowering-+.f64 |
| 1704× | +-lowering-+.f32 |
| 1510× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 464 | 3734 |
| 1 | 1542 | 3404 |
| 2 | 5023 | 3386 |
| 0 | 8172 | 3386 |
| 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (* (cos (* 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 (- (* 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)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 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)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 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)))))))))) |
(* (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 (- (* 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 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 (* 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)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* 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)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin 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))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (- 1/6 (/ 1 (pow x 2)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(* 1/6 (pow x 3)) |
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* -1/6 (pow x 3)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/6 (pow x 3)) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2))))))))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin 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))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps 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 (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 (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (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 eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(/ 1 (sin eps)) |
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin x)) |
(+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(sin (neg eps)) |
(+ (sin (neg eps)) (* x (cos (neg eps)))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps))))))) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps))))))))) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (neg (+ eps (* -1 x)))) |
(sin (neg (+ eps (* -1 x)))) |
(sin (neg (+ eps (* -1 x)))) |
(sin (neg (+ eps (* -1 x)))) |
(sin x) |
(+ (sin x) (* -1 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x)))))))) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (- x eps)) |
(sin (+ x (* -1 eps))) |
(sin (+ x (* -1 eps))) |
(sin (+ x (* -1 eps))) |
(sin (+ x (* -1 eps))) |
(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))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 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)))) |
(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))))) |
(cos (* 1/2 (+ 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)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 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 (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #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)))))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 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)))))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (+.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 1/2 (* eps (cos x))) |
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64)) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.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 (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.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 (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64))))))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #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)))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))) |
(+ (* 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)))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/6 binary64))))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (*.f64 eps (*.f64 eps #s(literal -1/5040 binary64))))))))) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) #s(literal -1 binary64))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(* (pow x 3) (- 1/6 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))) |
(*.f64 (*.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (-.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x)))) (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (-.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x)))) (*.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (sin.f64 x) (-.f64 (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) (-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 eps)))))))) |
(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)) |
(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)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))) |
(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)) |
(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 |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) #s(literal 1 binary64))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) #s(literal 1 binary64))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) #s(literal 1 binary64))) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) #s(literal 1 binary64))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(* -1/6 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(* -1/6 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+.f64 eps (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))) (*.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* eps x))) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps x)) |
(*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) (*.f64 eps (*.f64 x x))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps (*.f64 #s(literal -1/240 binary64) (*.f64 x x))) (*.f64 eps #s(literal 1/12 binary64)))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2))))))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/240 binary64)) (*.f64 eps (*.f64 (*.f64 x x) #s(literal 1/10080 binary64)))))))))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) #s(literal -1 binary64))))) |
(- (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 (* -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)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))) |
(- (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 (- 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 eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 eps)))))))) |
(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)) |
(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)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))) |
(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)) |
(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)) |
(/ 1 (sin eps)) |
(/.f64 #s(literal 1 binary64) (sin.f64 eps)) |
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (/.f64 (*.f64 x (cos.f64 eps)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 x (-.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))))) (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 x (-.f64 (*.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64)))) (*.f64 x (+.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64)))) (/.f64 (cos.f64 eps) (sin.f64 eps))) (*.f64 (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))) (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin x)) |
(/.f64 #s(literal 1 binary64) (sin.f64 x)) |
(+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (*.f64 eps (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 eps (-.f64 (*.f64 eps (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(sin (neg eps)) |
(-.f64 #s(literal 0 binary64) (sin.f64 eps)) |
(+ (sin (neg eps)) (* x (cos (neg eps)))) |
(-.f64 (*.f64 x (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps))))))) |
(-.f64 (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))))) (sin.f64 eps)) |
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps))))))))) |
(-.f64 (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 eps))) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)))))) (sin.f64 eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (neg (+ eps (* -1 x)))) |
(sin.f64 (-.f64 x eps)) |
(sin (neg (+ eps (* -1 x)))) |
(sin.f64 (-.f64 x eps)) |
(sin (neg (+ eps (* -1 x)))) |
(sin.f64 (-.f64 x eps)) |
(sin (neg (+ eps (* -1 x)))) |
(sin.f64 (-.f64 x eps)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* -1 (* eps (cos x)))) |
(-.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x)))))) |
(+.f64 (sin.f64 x) (*.f64 eps (-.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))) |
(+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x)))))))) |
(+.f64 (sin.f64 x) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/6 binary64)))) (cos.f64 x)))) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x eps)) |
(sin.f64 (-.f64 x eps)) |
(sin (- x 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)) |
(sin (+ x (* -1 eps))) |
(sin.f64 (-.f64 x eps)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64))) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* -1/6 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps x) |
(*.f64 eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(*.f64 x (+.f64 eps (*.f64 eps (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(*.f64 x (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 #s(literal 1/120 binary64) (*.f64 x x))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(*.f64 x (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (*.f64 eps #s(literal 1/120 binary64))))))))) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
Compiled 20003 to 2132 computations (89.3% saved)
26 alts after pruning (23 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 946 | 18 | 964 |
| Fresh | 1 | 5 | 6 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 950 | 26 | 976 |
| Status | Accuracy | Program |
|---|---|---|
| 61.7% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) | |
| 36.4% | (/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) | |
| 55.1% | (/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) | |
| ✓ | 36.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| 60.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) | |
| 61.7% | (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| ✓ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.4% | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
| 97.7% | (+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) | |
| 96.8% | (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) | |
| ▶ | 99.6% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| 99.6% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.5% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.3% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 5.8% | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) | |
| 99.4% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| 99.4% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) | |
| ▶ | 98.6% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
| ✓ | 99.3% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) | |
| ▶ | 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
| 96.8% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) | |
| 96.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) | |
| 5.5% | (*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) | |
| 98.6% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 96.7% | eps |
Compiled 801 to 507 computations (36.7% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 eps (sin.f64 x)) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 128 | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| 4960× | +-lowering-+.f64 |
| 4960× | +-lowering-+.f32 |
| 3668× | *-lowering-*.f32 |
| 3668× | *-lowering-*.f64 |
| 2620× | distribute-lft-in |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 300 |
| 1 | 116 | 272 |
| 2 | 369 | 271 |
| 3 | 1222 | 271 |
| 4 | 3317 | 271 |
| 5 | 4686 | 271 |
| 6 | 5243 | 271 |
| 7 | 5625 | 271 |
| 8 | 5654 | 271 |
| 9 | 5654 | 271 |
| 0 | 8246 | 271 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) |
eps |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))) |
1/2 |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))) |
(* eps eps) |
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))) |
-1/48 |
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))) |
(+ 1/3840 (* eps (* eps -1/645120))) |
1/3840 |
(* eps (* eps -1/645120)) |
(* eps -1/645120) |
-1/645120 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
2 |
eps |
(* eps (+ 1 (* x (* -1/2 (+ eps x))))) |
eps |
(+ 1 (* x (* -1/2 (+ eps x)))) |
1 |
(* x (* -1/2 (+ eps x))) |
x |
(* -1/2 (+ eps x)) |
-1/2 |
(+ eps x) |
(* eps (+ (cos x) (* eps (* x -1/2)))) |
eps |
(+ (cos x) (* eps (* x -1/2))) |
(cos x) |
x |
(* eps (* x -1/2)) |
(* x -1/2) |
-1/2 |
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x))) |
(* (* eps (sin x)) (* eps -1/2)) |
(* eps (sin x)) |
eps |
(sin x) |
x |
(* eps -1/2) |
-1/2 |
(* eps (cos x)) |
(cos x) |
| Outputs |
|---|
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) |
eps |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) |
1/2 |
#s(literal 1/2 binary64) |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) |
(* eps eps) |
(*.f64 eps eps) |
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))) |
(+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
-1/48 |
#s(literal -1/48 binary64) |
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
(+ 1/3840 (* eps (* eps -1/645120))) |
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) |
1/3840 |
#s(literal 1/3840 binary64) |
(* eps (* eps -1/645120)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* eps -1/645120) |
(*.f64 eps #s(literal -1/645120 binary64)) |
-1/645120 |
#s(literal -1/645120 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(/ (+ eps (* x 2)) 2) |
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
(+ eps (* x 2)) |
(+.f64 eps (*.f64 x #s(literal 2 binary64))) |
(* x 2) |
(*.f64 x #s(literal 2 binary64)) |
x |
2 |
#s(literal 2 binary64) |
eps |
(* eps (+ 1 (* x (* -1/2 (+ eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
eps |
(+ 1 (* x (* -1/2 (+ eps x)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) |
1 |
#s(literal 1 binary64) |
(* x (* -1/2 (+ eps x))) |
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) |
x |
(* -1/2 (+ eps x)) |
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) |
-1/2 |
#s(literal -1/2 binary64) |
(+ eps x) |
(+.f64 eps x) |
(* eps (+ (cos x) (* eps (* x -1/2)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
eps |
(+ (cos x) (* eps (* x -1/2))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(cos x) |
(cos.f64 x) |
x |
(* eps (* x -1/2)) |
(*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
(* x -1/2) |
(*.f64 x #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* (* eps (sin x)) (* eps -1/2)) |
(*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
eps |
(sin x) |
(sin.f64 x) |
x |
(* eps -1/2) |
(*.f64 eps #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(cos x) |
(cos.f64 x) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps (cos.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (sin.f64 x)) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
| ✓ | accuracy | 100.0% | (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) |
| ✓ | accuracy | 99.7% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) |
| 134.0ms | 256× | 0 | valid |
Compiled 304 to 41 computations (86.5% saved)
ival-mult: 32.0ms (49.6% of total)ival-add: 12.0ms (18.6% of total)...c/correct-round.rkt:119:19: 10.0ms (15.5% of total)ival-cos: 5.0ms (7.7% of total)ival-div: 2.0ms (3.1% of total)ival-sin: 2.0ms (3.1% of total)const: 1.0ms (1.5% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))> |
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))> |
#<alt (* eps (+ 1 (* x (* -1/2 (+ eps x)))))> |
#<alt (+ 1 (* x (* -1/2 (+ eps x))))> |
#<alt (* x (* -1/2 (+ eps x)))> |
#<alt (* -1/2 (+ eps x))> |
#<alt (* eps (+ (cos x) (* eps (* x -1/2))))> |
#<alt (+ (cos x) (* eps (* x -1/2)))> |
#<alt (cos x)> |
#<alt (* eps (* x -1/2))> |
#<alt (+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))> |
#<alt (* (* eps (sin x)) (* eps -1/2))> |
#<alt (* eps (sin x))> |
#<alt (sin x)> |
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
#<alt (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))> |
#<alt (* eps (* eps -1/645120))> |
#<alt (* eps (cos x))> |
| Outputs |
|---|
#<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 (* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))> |
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))> |
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<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 (* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 7) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))> |
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))> |
#<alt (* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))> |
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<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 (* -1/645120 (pow eps 7))> |
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* -1/645120 (pow eps 7))> |
#<alt (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/48 (pow eps 2)))> |
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))> |
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1/2 x)> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (* -1/2 eps)> |
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))> |
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))> |
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))> |
#<alt (* -1/2 eps)> |
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))> |
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))> |
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))> |
#<alt (* -1/2 eps)> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* -1/2 x)> |
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))> |
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))> |
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2)))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))> |
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))> |
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))> |
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps x)))> |
#<alt (+ (cos x) (* -1/2 (* eps x)))> |
#<alt (+ (cos x) (* -1/2 (* eps x)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps x)> |
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))> |
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))> |
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin x))> |
#<alt (* eps (sin 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 x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<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 (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 (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 (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 (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 (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 (* 1/3840 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<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))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<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))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* eps (pow x 2))))> |
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))> |
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
105 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | (+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x))) |
| 5.0ms | eps | @ | -inf | (* eps (+ 1 (* x (* -1/2 (+ eps x))))) |
| 3.0ms | x | @ | 0 | (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 3.0ms | eps | @ | -inf | (+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x))) |
| 2.0ms | x | @ | inf | (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1× | batch-egg-rewrite |
| 5474× | *-lowering-*.f32 |
| 5474× | *-lowering-*.f64 |
| 3694× | /-lowering-/.f32 |
| 3694× | /-lowering-/.f64 |
| 1846× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 230 |
| 1 | 224 | 207 |
| 2 | 1976 | 206 |
| 0 | 9380 | 206 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))) |
(* eps (+ 1 (* x (* -1/2 (+ eps x))))) |
(+ 1 (* x (* -1/2 (+ eps x)))) |
(* x (* -1/2 (+ eps x))) |
(* -1/2 (+ eps x)) |
(* eps (+ (cos x) (* eps (* x -1/2)))) |
(+ (cos x) (* eps (* x -1/2))) |
(cos x) |
(* eps (* x -1/2)) |
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x))) |
(* (* eps (sin x)) (* eps -1/2)) |
(* eps (sin x)) |
(sin x) |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))) |
(cos (/ (+ eps (* x 2)) 2)) |
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))) |
(* eps (* eps -1/645120)) |
(* eps (cos x)) |
| Outputs |
|---|
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) |
(*.f64 eps (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) |
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) eps) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) |
(+.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(fma.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) |
(fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) |
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) eps) |
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(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/56623104000 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/268485921865728000 binary64))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (neg.f64 (-.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/56623104000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/268485921865728000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/416179814400 binary64))))) (neg.f64 (-.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/56623104000 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/268485921865728000 binary64)))) (*.f64 eps eps))) (neg.f64 (+.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/416179814400 binary64))) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/268485921865728000 binary64))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (*.f64 #s(literal 1/56623104000 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) (+.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) |
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
(*.f64 (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) (*.f64 eps eps)) |
(*.f64 (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) eps) |
(*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(*.f64 #s(literal -1/645120 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal -1/645120 binary64)) eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
| 1× | egg-herbie |
| 5638× | *-lowering-*.f32 |
| 5638× | *-lowering-*.f64 |
| 2114× | +-lowering-+.f64 |
| 2114× | +-lowering-+.f32 |
| 1556× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 473 | 4972 |
| 1 | 1688 | 4537 |
| 2 | 6130 | 4516 |
| 0 | 8045 | 4516 |
| 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)) (* 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)))))))))) |
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))) |
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))) |
(* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 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)))))))))) |
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 7) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))) |
(* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))) |
(* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))) |
(* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* 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)))) |
(* -1/645120 (pow eps 7)) |
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 7)) |
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))) |
1/2 |
(+ 1/2 (* -1/48 (pow eps 2))) |
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))) |
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* eps x)) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* -1/2 (* eps x)) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1/2 x) |
(+ (* -1/2 eps) (* -1/2 x)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* -1/2 eps) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* -1/2 eps) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* -1/2 x)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* -1/2 x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(* -1/2 x) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps x)))) |
(* eps (+ (cos x) (* -1/2 (* eps x)))) |
(* eps (+ (cos x) (* -1/2 (* eps x)))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
(* -1/2 (* (pow eps 2) x)) |
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x))) |
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x))) |
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x))) |
(* -1/2 (* (pow eps 2) x)) |
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2))))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (/ (cos x) x))) |
(* x (+ (* -1/2 eps) (/ (cos x) x))) |
(* x (+ (* -1/2 eps) (/ (cos x) x))) |
(* -1/2 (* eps x)) |
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps)))) |
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps)))) |
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps)))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps x))) |
(+ (cos x) (* -1/2 (* eps x))) |
(+ (cos x) (* -1/2 (* eps x))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (/ (cos x) eps))) |
(* eps (+ (* -1/2 x) (/ (cos x) eps))) |
(* eps (+ (* -1/2 x) (/ (cos x) eps))) |
(* -1/2 (* eps x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x)))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) x)) |
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2))))))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
(* eps (sin x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(* -1/48 (pow eps 2)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(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))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 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)))) |
(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))))) |
(cos (* 1/2 (+ 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)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(* 1/3840 (pow eps 2)) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* -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)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* -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)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 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 (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))) |
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 #s(literal -1/322560 binary64) (*.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (+.f64 (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64))))))) |
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 #s(literal -1/322560 binary64) (*.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (neg.f64 (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))) |
(*.f64 (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))) (neg.f64 (pow.f64 eps #s(literal 7 binary64)))) |
(* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))) |
(*.f64 (-.f64 (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (neg.f64 (pow.f64 eps #s(literal 7 binary64)))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
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(cos x) |
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(cos x) |
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(* -1/2 (* eps x)) |
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(* eps (cos x)) |
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(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
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eps |
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(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2))))))))) |
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(* -1/2 (* (pow eps 2) (sin x))) |
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(* eps x) |
(*.f64 eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
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x |
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(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
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(cos x) |
(cos.f64 x) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
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(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
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(* -1/645120 (pow eps 4)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/645120 binary64)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps (*.f64 (*.f64 x x) #s(literal -1/720 binary64))) (*.f64 eps #s(literal 1/24 binary64)))))))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
Compiled 25271 to 2301 computations (90.9% saved)
31 alts after pruning (26 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 827 | 12 | 839 |
| Fresh | 4 | 14 | 18 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 3 | 3 |
| Total | 834 | 31 | 865 |
| Status | Accuracy | Program |
|---|---|---|
| 61.7% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) | |
| 36.4% | (/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) | |
| 33.9% | (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) | |
| 55.1% | (/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) | |
| ✓ | 36.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| ▶ | 60.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
| 61.7% | (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| ✓ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ✓ | 99.4% | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
| 97.7% | (+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) | |
| 96.8% | (+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) | |
| 99.6% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) | |
| 99.6% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.5% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.3% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.6% | (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
| 5.0% | (*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) | |
| 97.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) | |
| 99.4% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| 99.4% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) | |
| ✓ | 99.3% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| ▶ | 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) | |
| 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) | |
| 97.5% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) | |
| 96.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) | |
| 97.3% | (*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) | |
| ▶ | 5.5% | (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| 5.5% | (*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) | |
| ▶ | 98.6% | (*.f64 eps (cos.f64 x)) |
| ✓ | 96.7% | eps |
Compiled 1121 to 663 computations (40.9% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 eps x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
| ✓ | cost-diff | 256 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) |
| ✓ | cost-diff | 256 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 eps (cos.f64 x)) |
| ✓ | cost-diff | 0 | (*.f64 eps #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 256 | (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))) |
| ✓ | cost-diff | 256 | (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))) |
| ✓ | cost-diff | 256 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 eps #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
| 2820× | +-lowering-+.f64 |
| 2820× | +-lowering-+.f32 |
| 2538× | *-lowering-*.f32 |
| 2538× | *-lowering-*.f64 |
| 1646× | sum3-define |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 270 |
| 1 | 119 | 245 |
| 2 | 396 | 245 |
| 3 | 1359 | 245 |
| 4 | 3704 | 236 |
| 5 | 5309 | 236 |
| 6 | 6970 | 236 |
| 0 | 8096 | 236 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) |
(cos (+ x (* eps 1/2))) |
(+ x (* eps 1/2)) |
x |
(* eps 1/2) |
eps |
1/2 |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))) |
(* eps eps) |
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) |
-1/48 |
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))) |
(+ 1/3840 (* (* eps eps) -1/645120)) |
1/3840 |
(* (* eps eps) -1/645120) |
-1/645120 |
(* eps 2) |
2 |
(* eps (* eps (* x -1/2))) |
eps |
(* eps (* x -1/2)) |
(* x -1/2) |
x |
-1/2 |
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))) |
eps |
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))) |
1 |
(* (* eps -1/2) (+ x (/ (* x x) eps))) |
(* eps -1/2) |
-1/2 |
(+ x (/ (* x x) eps)) |
x |
(/ (* x x) eps) |
(* x x) |
(* eps (cos x)) |
eps |
(cos x) |
x |
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x)) |
(/ 1 (/ 1 (sin (+ eps x)))) |
1 |
(/ 1 (sin (+ eps x))) |
(sin (+ eps x)) |
(+ eps x) |
eps |
x |
(sin x) |
| Outputs |
|---|
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) |
(cos (+ x (* eps 1/2))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(+ x (* eps 1/2)) |
(+.f64 x (*.f64 eps #s(literal 1/2 binary64))) |
x |
(* eps 1/2) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) |
(* eps eps) |
(*.f64 eps eps) |
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))) |
(+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) |
-1/48 |
#s(literal -1/48 binary64) |
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))) |
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
(+ 1/3840 (* (* eps eps) -1/645120)) |
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))) |
1/3840 |
#s(literal 1/3840 binary64) |
(* (* eps eps) -1/645120) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
-1/645120 |
#s(literal -1/645120 binary64) |
(* eps 2) |
(*.f64 eps #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
(* eps (* eps (* x -1/2))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x eps))) |
eps |
(* eps (* x -1/2)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 x eps)) |
(* x -1/2) |
(*.f64 x #s(literal -1/2 binary64)) |
x |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))))) |
eps |
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)))) |
1 |
#s(literal 1 binary64) |
(* (* eps -1/2) (+ x (/ (* x x) eps))) |
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))) |
(* eps -1/2) |
(*.f64 eps #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(+ x (/ (* x x) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
x |
(/ (* x x) eps) |
(/.f64 (*.f64 x x) eps) |
(* x x) |
(*.f64 x x) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
eps |
(cos x) |
(cos.f64 x) |
x |
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(/ 1 (/ 1 (sin (+ eps x)))) |
(sin.f64 (+.f64 x eps)) |
1 |
#s(literal 1 binary64) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(+ eps x) |
(+.f64 x eps) |
eps |
x |
(sin x) |
(sin.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 eps x)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) |
| ✓ | accuracy | 61.7% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (*.f64 eps (cos.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
| ✓ | accuracy | 99.8% | (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))) |
| ✓ | accuracy | 99.6% | (+.f64 x (/.f64 (*.f64 x x) eps)) |
| ✓ | accuracy | 57.4% | (/.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | accuracy | 99.9% | (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | accuracy | 99.8% | (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
| ✓ | accuracy | 99.7% | (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) |
| 144.0ms | 152× | 1 | valid |
| 41.0ms | 101× | 0 | valid |
| 4.0ms | 3× | 2 | valid |
Compiled 282 to 41 computations (85.5% saved)
ival-mult: 51.0ms (42.2% of total)...c/correct-round.rkt:119:19: 18.0ms (14.9% of total)ival-add: 14.0ms (11.6% of total)backward-pass: 11.0ms (9.1% of total)ival-div: 9.0ms (7.4% of total)ival-cos: 8.0ms (6.6% of total)ival-sin: 6.0ms (5% of total)ival-sub: 2.0ms (1.7% of total)const: 1.0ms (0.8% of total)| Inputs |
|---|
#<alt (* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))> |
#<alt (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))> |
#<alt (cos (+ x (* eps 1/2)))> |
#<alt (+ x (* eps 1/2))> |
#<alt (* eps (* eps (* x -1/2)))> |
#<alt (* eps (* x -1/2))> |
#<alt (* x -1/2)> |
#<alt (* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))> |
#<alt (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))> |
#<alt (* (* eps -1/2) (+ x (/ (* x x) eps)))> |
#<alt (* eps -1/2)> |
#<alt (* eps (cos x))> |
#<alt (cos x)> |
#<alt (- (/ 1 (/ 1 (sin (+ eps x)))) (sin x))> |
#<alt (/ 1 (/ 1 (sin (+ eps x))))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (sin (+ eps x))> |
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))> |
#<alt (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))> |
#<alt (* (* eps eps) -1/645120)> |
#<alt (/ (* x x) eps)> |
#<alt (+ x (/ (* x x) eps))> |
| Outputs |
|---|
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 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 (* -1/322560 (* (pow eps 7) (cos (+ x (* 1/2 eps)))))> |
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))))> |
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (+ (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (/ (cos (+ x (* 1/2 eps))) (pow eps 6))))))> |
#<alt (* -1/322560 (* (pow eps 7) (cos (- x (* -1/2 eps)))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/322560 (cos (- x (* -1/2 eps)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 6))) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4))))))))> |
#<alt (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (+ (* -1 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* -1/2 (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* 1/6 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (* 1/2 (cos x))> |
#<alt (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))> |
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))> |
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))> |
#<alt (* -1/645120 (* (pow eps 6) (cos (+ x (* 1/2 eps)))))> |
#<alt (* (pow eps 6) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))))> |
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (+ (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 6)))))))> |
#<alt (* -1/645120 (* (pow eps 6) (cos (- x (* -1/2 eps)))))> |
#<alt (* (pow eps 6) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))> |
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (+ (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 6)))))))> |
#<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 (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 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 (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 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 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 x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x 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 (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* -1/2 eps)> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* eps (pow x 2))))> |
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))> |
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (cos x))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (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 (- (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 (* -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) (* 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 x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps 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 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (/ 1 (sin x))> |
#<alt (+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))> |
#<alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))> |
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin (- x (* -1 eps))))> |
#<alt (/ 1 (sin eps))> |
#<alt (+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (+ eps x)))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 x))))> |
#<alt (/ 1 (sin (- eps (* -1 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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<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 (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* -1/645120 (pow eps 6))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))> |
#<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))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<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))> |
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (* -1/645120 (pow eps 2))> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (pow x 2) eps)> |
#<alt x> |
#<alt (* x (+ 1 (/ x eps)))> |
#<alt (* x (+ 1 (/ x eps)))> |
#<alt (* x (+ 1 (/ x eps)))> |
#<alt (/ (pow x 2) eps)> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (/ (pow x 2) eps)> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (+ (* eps x) (pow x 2)) eps)> |
#<alt (/ (+ (* eps x) (pow x 2)) eps)> |
#<alt (/ (+ (* eps x) (pow x 2)) eps)> |
#<alt x> |
#<alt (+ x (/ (pow x 2) eps))> |
#<alt (+ x (/ (pow x 2) eps))> |
#<alt (+ x (/ (pow x 2) eps))> |
#<alt x> |
#<alt (+ x (/ (pow x 2) eps))> |
#<alt (+ x (/ (pow x 2) eps))> |
#<alt (+ x (/ (pow x 2) eps))> |
114 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | inf | (* (* eps -1/2) (+ x (/ (* x x) eps))) |
| 1.0ms | x | @ | -inf | (* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
| 1.0ms | x | @ | inf | (* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
| 1.0ms | eps | @ | 0 | (* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))) |
| 1.0ms | eps | @ | inf | (* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
| 1× | batch-egg-rewrite |
| 3384× | *-lowering-*.f32 |
| 3384× | *-lowering-*.f64 |
| 2534× | fma-lowering-fma.f32 |
| 2534× | fma-lowering-fma.f64 |
| 2164× | /-lowering-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 195 |
| 1 | 250 | 176 |
| 2 | 2203 | 176 |
| 0 | 8592 | 176 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2)) |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) |
(cos (+ x (* eps 1/2))) |
(+ x (* eps 1/2)) |
(* eps (* eps (* x -1/2))) |
(* eps (* x -1/2)) |
(* x -1/2) |
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))) |
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))) |
(* (* eps -1/2) (+ x (/ (* x x) eps))) |
(* eps -1/2) |
(* eps (cos x)) |
(cos x) |
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x)) |
(/ 1 (/ 1 (sin (+ eps x)))) |
(/ 1 (sin (+ eps x))) |
(sin (+ eps x)) |
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))) |
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))) |
(* (* eps eps) -1/645120) |
(/ (* x x) eps) |
(+ x (/ (* x x) eps)) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal 2 binary64))) (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64)))) |
(fma.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64)))) |
(*.f64 eps (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))) |
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(*.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (/.f64 x eps) x) |
(+.f64 x (/.f64 (*.f64 x x) eps)) |
(+.f64 (/.f64 (*.f64 x x) eps) x) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (*.f64 x x) eps))) (/.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (-.f64 x (/.f64 (*.f64 x x) eps)))) |
(fma.f64 x (/.f64 x eps) x) |
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps) x) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) eps) x) |
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) x) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 x x) x) |
(fma.f64 (/.f64 x eps) x x) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))))))) |
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x))))) |
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (-.f64 (*.f64 x x) (/.f64 x (/.f64 eps (*.f64 x x)))))) |
(/.f64 (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x)))) (-.f64 x (/.f64 (*.f64 x x) eps))) |
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x)))))) |
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (+.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (-.f64 (*.f64 x x) (/.f64 x (/.f64 eps (*.f64 x x))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))))) (neg.f64 (-.f64 x (/.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (*.f64 x x)) (-.f64 (/.f64 (*.f64 x x) eps) x)) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x (/.f64 (*.f64 x x) eps))) (*.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))))) (*.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) (-.f64 x (/.f64 (*.f64 x x) eps)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x)))))) (neg.f64 (neg.f64 (-.f64 x (/.f64 (*.f64 x x) eps))))) |
(/.f64 (neg.f64 (-.f64 (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))) (*.f64 x x))) (neg.f64 (-.f64 (/.f64 (*.f64 x x) eps) x))) |
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 x (/.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x))))) #s(literal -1 binary64)) |
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (*.f64 x x) eps) x) (/.f64 eps (*.f64 x x)))))) |
(*.f64 (-.f64 (*.f64 x x) (/.f64 (/.f64 (*.f64 x x) eps) (/.f64 eps (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 x (/.f64 (*.f64 x x) eps)))) |
| 1× | egg-herbie |
| 5380× | *-lowering-*.f32 |
| 5380× | *-lowering-*.f64 |
| 1868× | +-lowering-+.f64 |
| 1868× | +-lowering-+.f32 |
| 1314× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 469 | 4646 |
| 1 | 1613 | 4339 |
| 2 | 5494 | 4327 |
| 0 | 8690 | 4327 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 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)))))))))) |
(* -1/322560 (* (pow eps 7) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 7) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))) |
(* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (+ (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (/ (cos (+ x (* 1/2 eps))) (pow eps 6)))))) |
(* -1/322560 (* (pow eps 7) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/322560 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4))))))) |
(* -1 (* (pow eps 7) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 6))) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4)))))))) |
(* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(+ (* -1 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* -1/2 (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* 1/6 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* 1/2 (cos x)) |
(+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))) |
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))) |
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))) |
(* -1/645120 (* (pow eps 6) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 6) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))) |
(* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (+ (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 6))))))) |
(* -1/645120 (* (pow eps 6) (cos (- x (* -1/2 eps))))) |
(* (pow eps 6) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))) |
(* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))) |
(* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (+ (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 6))))))) |
(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))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 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))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x 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))) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* (pow eps 2) x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 (* eps x)) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* eps x)) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps)))) |
(* -1/2 (* eps x)) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* -1/2 eps) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* 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 (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (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 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps 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) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(/ 1 (sin x)) |
(+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/ 1 (sin eps)) |
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (+ eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/ 1 (sin (- eps (* -1 x)))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(* -1/48 (pow eps 2)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 6)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* 1/3840 (pow eps 2)) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(* -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)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* -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)) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(* -1/645120 (pow eps 2)) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
(/ (pow x 2) eps) |
x |
(* x (+ 1 (/ x eps))) |
(* x (+ 1 (/ x eps))) |
(* x (+ 1 (/ x eps))) |
(/ (pow x 2) eps) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(/ (pow x 2) eps) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(/ (pow x 2) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
x |
(+ x (/ (pow x 2) eps)) |
(+ x (/ (pow x 2) eps)) |
(+ x (/ (pow x 2) eps)) |
x |
(+ x (/ (pow x 2) eps)) |
(+ x (/ (pow x 2) eps)) |
(+ x (/ (pow x 2) eps)) |
| Outputs |
|---|
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 x (-.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal -2 binary64))) (*.f64 (*.f64 (*.f64 eps x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 x (+.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal -2 binary64))) (*.f64 x (-.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) eps) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) |
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(/ 1 (sin x)) |
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(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (sin.f64 x))) (*.f64 (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (/.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- x (* -1 eps)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin eps)) |
(/.f64 #s(literal 1 binary64) (sin.f64 eps)) |
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps))) |
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (/.f64 (*.f64 x (cos.f64 eps)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 x (-.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))))) (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 x (-.f64 (*.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64)))) (*.f64 x (+.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64)))) (/.f64 (cos.f64 eps) (sin.f64 eps))) (*.f64 (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))) (/.f64 (cos.f64 eps) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (+ eps x))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(/ 1 (sin (- eps (* -1 x)))) |
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))) |
(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)) |
(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)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))))) |
(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)) |
(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)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))) |
(* -1/645120 (pow eps 6)) |
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 6 binary64))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) |
(* -1/645120 (pow eps 6)) |
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 6 binary64))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) |
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) |
(* -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 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* -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 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
x |
(* x (+ 1 (/ x eps))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* x (+ 1 (/ x eps))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* x (+ 1 (/ x eps))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* (pow x 2) (+ (/ 1 eps) (/ 1 x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(/ (pow x 2) eps) |
(/.f64 (*.f64 x x) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
(/.f64 (*.f64 x (+.f64 eps x)) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
(/.f64 (*.f64 x (+.f64 eps x)) eps) |
(/ (+ (* eps x) (pow x 2)) eps) |
(/.f64 (*.f64 x (+.f64 eps x)) eps) |
x |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
x |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(+ x (/ (pow x 2) eps)) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
Compiled 22534 to 2242 computations (90.1% saved)
36 alts after pruning (27 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 890 | 12 | 902 |
| Fresh | 6 | 15 | 21 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 5 | 5 |
| Total | 897 | 36 | 933 |
| Status | Accuracy | Program |
|---|---|---|
| 61.7% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) | |
| 33.9% | (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) | |
| 55.1% | (/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) | |
| ✓ | 36.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| ✓ | 60.9% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
| 61.7% | (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| ✓ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ✓ | 99.4% | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
| 97.7% | (+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) | |
| 96.8% | (+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) | |
| 99.6% | (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) | |
| 99.8% | (*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.8% | (*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.3% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.6% | (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.5% | (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.6% | (*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) | |
| 5.0% | (*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) | |
| 97.7% | (*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) | |
| 97.7% | (*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) | |
| 99.4% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| 99.4% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) | |
| ✓ | 99.3% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) | |
| ✓ | 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) | |
| 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) | |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) | |
| 97.5% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) | |
| 96.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) | |
| 97.3% | (*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) | |
| ✓ | 5.5% | (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
| 5.5% | (*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) | |
| ✓ | 98.6% | (*.f64 eps (cos.f64 x)) |
| 61.5% | (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64))))) | |
| ✓ | 96.7% | eps |
Compiled 1820 to 738 computations (59.5% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) |
| Outputs |
|---|
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
3 calls:
| 14.0ms | eps |
| 13.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 13.0ms | 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 |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) |
| Outputs |
|---|
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
3 calls:
| 24.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 13.0ms | eps |
| 12.0ms | 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 |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x)) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
3 calls:
| 15.0ms | eps |
| 12.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 12.0ms | 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 |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64)))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x)) |
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x))) |
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps) |
| Outputs |
|---|
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
3 calls:
| 15.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 11.0ms | eps |
| 11.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
2 calls:
| 9.0ms | eps |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
2 calls:
| 12.0ms | eps |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
2 calls:
| 11.0ms | x |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
| Outputs |
|---|
(*.f64 eps (cos.f64 x)) |
2 calls:
| 7.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps)))) |
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))))) |
(sin.f64 eps) |
| Outputs |
|---|
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
2 calls:
| 10.0ms | eps |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.8% | 1 | x |
| 97.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64))))))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
2 calls:
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))) |
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))) |
| Outputs |
|---|
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
2 calls:
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
2 calls:
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x)))) |
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
2 calls:
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.5% | 1 | x |
| 97.5% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
2 calls:
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.8% | 1 | x |
| 96.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
2 calls:
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.7% | 1 | x |
| 96.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
Total -58.8b remaining (-2820.9%)
Threshold costs -58.8b (-2820.9%)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
| Outputs |
|---|
eps |
2 calls:
| 3.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.7% | 1 | x |
| 96.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 102× | *-commutative_binary64 |
| 52× | +-commutative_binary64 |
| 8× | sub-neg_binary64 |
| 6× | neg-sub0_binary64 |
| 6× | cancel-sign-sub-inv_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 97 | 279 |
| 1 | 179 | 279 |
| 2 | 190 | 279 |
| 3 | 195 | 279 |
| 4 | 197 | 279 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
eps |
| Outputs |
|---|
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))) |
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
eps |
| 5638× | *-lowering-*.f32 |
| 5638× | *-lowering-*.f64 |
| 5380× | *-lowering-*.f32 |
| 5380× | *-lowering-*.f64 |
| 4902× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 195 |
| 1 | 250 | 176 |
| 2 | 2203 | 176 |
| 0 | 8592 | 176 |
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 402 | 16 |
| 3 | 5232 | 16 |
| 0 | 8309 | 16 |
| 0 | 469 | 4646 |
| 1 | 1613 | 4339 |
| 2 | 5494 | 4327 |
| 0 | 8690 | 4327 |
| 0 | 473 | 4972 |
| 1 | 1688 | 4537 |
| 2 | 6130 | 4516 |
| 0 | 8045 | 4516 |
| 0 | 107 | 488 |
| 1 | 327 | 465 |
| 2 | 963 | 459 |
| 3 | 3572 | 459 |
| 0 | 8267 | 459 |
| 0 | 464 | 3734 |
| 1 | 1542 | 3404 |
| 2 | 5023 | 3386 |
| 0 | 8172 | 3386 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node 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 |
| 1× | iter limit |
| 1× | node limit |
Compiled 861 to 486 computations (43.6% saved)
Compiled 612 to 224 computations (63.4% saved)
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