
Time bar (total: 15.3s)
| 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-add: 8.0ms (19.7% of total)ival-sin: 8.0ms (19.7% of total)...c/correct-round.rkt:119:19: 7.0ms (17.2% of total)ival-mult: 6.0ms (14.8% of total)ival-fabs: 3.0ms (7.4% of total)ival-sub: 2.0ms (4.9% of total)ival-and: 2.0ms (4.9% of total)ival-<=: 2.0ms (4.9% of total)ival-<: 2.0ms (4.9% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 3.6s | 26089× | 0 | precondition |
| 1.3s | 4457× | 1 | valid |
| 517.0ms | 3799× | 0 | valid |
...c/correct-round.rkt:119:19: 784.0ms (21.1% of total)ival-sin: 685.0ms (18.4% of total)ival-mult: 403.0ms (10.8% of total)ival-<: 337.0ms (9.1% of total)ival-add: 325.0ms (8.7% of total)ival-fabs: 317.0ms (8.5% of total)ival-<=: 296.0ms (8% of total)ival-sub: 224.0ms (6% of total)ival-and: 161.0ms (4.3% of total)backward-pass: 132.0ms (3.6% of total)const: 53.0ms (1.4% 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 | 50 | 42 |
| 2 | 101 | 42 |
| 3 | 207 | 42 |
| 4 | 513 | 42 |
| 5 | 923 | 42 |
| 6 | 1310 | 42 |
| 7 | 1574 | 42 |
| 8 | 1710 | 42 |
| 9 | 1737 | 42 |
| 0 | 6 | 7 |
| 1 | 11 | 7 |
| 2 | 16 | 7 |
| 3 | 23 | 7 |
| 4 | 33 | 7 |
| 5 | 65 | 7 |
| 6 | 124 | 7 |
| 7 | 212 | 7 |
| 8 | 297 | 7 |
| 9 | 403 | 7 |
| 10 | 481 | 7 |
| 11 | 487 | 7 |
| 0 | 487 | 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)) |
(- (fast-sin (+ x eps)) (fast-sin x)) |
(- (sin (+ (neg x) eps)) (sin (neg x))) |
(+ (fast-sin x) (fast-sin (- eps x))) |
(- (sin (+ x (neg eps))) (sin x)) |
(- (fast-sin (- x eps)) (fast-sin x)) |
(neg (- (sin (+ (neg x) eps)) (sin (neg x)))) |
(- (fast-sin (- x eps)) (fast-sin x)) |
(neg (- (sin (+ x (neg eps))) (sin x))) |
(+ (fast-sin x) (fast-sin (- eps x))) |
(- (sin (+ eps x)) (sin eps)) |
(- (fast-sin (+ x eps)) (fast-sin eps)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 227 | 2 | (-3.462796699570995e-167 2.764054764814959e-169) | 3 | (-7.668690385135368e-163 1.2576926385947832e-164) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1 | 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 | 268× | 1 | valid |
| 25.0ms | 244× | 0 | valid |
Compiled 51 to 20 computations (60.8% saved)
ival-sin: 11.0ms (39.6% of total)ival-add: 6.0ms (21.6% of total)backward-pass: 6.0ms (21.6% of total)ival-sub: 4.0ms (14.4% of total)const: 1.0ms (3.6% of total)Compiled 9 to 6 computations (33.3% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.8% | (-.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 | 11 | 18 |
| 2 | 16 | 18 |
| 3 | 23 | 18 |
| 4 | 33 | 18 |
| 5 | 65 | 18 |
| 6 | 124 | 18 |
| 7 | 212 | 18 |
| 8 | 297 | 18 |
| 9 | 403 | 18 |
| 10 | 481 | 18 |
| 11 | 487 | 18 |
| 0 | 487 | 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 | 99.9% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 62.9% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 34.0ms | 134× | 1 | valid |
| 12.0ms | 122× | 0 | valid |
Compiled 21 to 7 computations (66.7% saved)
ival-sin: 6.0ms (44.5% of total)ival-add: 3.0ms (22.2% of total)backward-pass: 3.0ms (22.2% of total)ival-sub: 2.0ms (14.8% 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 | eps | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (sin x) |
| 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 | 51 | 16 |
| 2 | 413 | 16 |
| 3 | 5315 | 16 |
| 0 | 8737 | 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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x))))))) |
(+.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 #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 (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 (+.f64 x eps)) (sin.f64 x)))))) |
(-.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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x))))))) |
(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 #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))))) (neg.f64 (/.f64 (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 (+.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 #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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x))))))) |
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x))))))) |
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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 (*.f64 (sin.f64 x) (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 eps (*.f64 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 eps (*.f64 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 eps (*.f64 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 | 334 | 459 |
| 2 | 972 | 455 |
| 3 | 3571 | 455 |
| 0 | 8279 | 455 |
| 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 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) eps))) |
(- (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 (*.f64 eps 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 (*.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) 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 (- 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 x (*.f64 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 7061 to 729 computations (89.7% saved)
13 alts after pruning (12 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 249 | 12 | 261 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 249 | 13 | 262 |
| Status | Accuracy | Program |
|---|---|---|
| 62.8% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) | |
| 37.1% | (-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x)) | |
| 62.9% | (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| 61.7% | (-.f64 (sin.f64 (+.f64 x eps)) (*.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)))))))) | |
| ▶ | 61.8% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))))) |
| ▶ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 62.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.8% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| ▶ | 99.9% | (*.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)) |
| 99.2% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) | |
| ▶ | 98.8% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 97.7% | (sin.f64 eps) |
Compiled 377 to 252 computations (33.2% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | 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 (+.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)))))))))) |
| ✓ | 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 (+.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))))))))))) |
| ✓ | 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 | 0 | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 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)))) |
| ✓ | cost-diff | 0 | (*.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)) |
| ✓ | cost-diff | 128 | (+.f64 eps #s(literal 0 binary64)) |
| 2494× | *-lowering-*.f32 |
| 2494× | *-lowering-*.f64 |
| 1604× | +-lowering-+.f64 |
| 1604× | +-lowering-+.f32 |
| 1306× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 43 | 280 |
| 1 | 120 | 253 |
| 2 | 381 | 249 |
| 3 | 1327 | 249 |
| 4 | 3923 | 249 |
| 5 | 6821 | 249 |
| 0 | 8232 | 249 |
| 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 |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))) |
1 |
(* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))) |
(* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))) |
-1/6 |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(* x x) |
(+ 1/120 (* x (* x -1/5040))) |
1/120 |
(* x (* x -1/5040)) |
(* x -1/5040) |
-1/5040 |
(* 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) |
| 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) |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))) |
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))))))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))))) |
(+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))))) |
1 |
#s(literal 1 binary64) |
(* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) |
(* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(*.f64 x (-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))))) |
(+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))) |
(-.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)))) |
-1/6 |
#s(literal -1/6 binary64) |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) |
(* x x) |
(*.f64 x x) |
(+ 1/120 (* x (* x -1/5040))) |
(+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))) |
1/120 |
#s(literal 1/120 binary64) |
(* x (* x -1/5040)) |
(*.f64 x (*.f64 x #s(literal -1/5040 binary64))) |
(* x -1/5040) |
(*.f64 x #s(literal -1/5040 binary64)) |
-1/5040 |
#s(literal -1/5040 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 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(cos x) |
(cos.f64 x) |
x |
(* -1/2 (* eps (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 (cos.f64 x) (*.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 | 100.0% | (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 eps (sin.f64 x)) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 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)))))))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) |
| ✓ | accuracy | 99.5% | (*.f64 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))))))) |
| ✓ | accuracy | 62.9% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))))) |
| ✓ | accuracy | 99.9% | (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 | 62.9% | (-.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% | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (*.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)) |
| ✓ | 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 | 99.9% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| 192.0ms | 134× | 1 | valid |
| 71.0ms | 122× | 0 | valid |
Compiled 318 to 44 computations (86.2% saved)
ival-mult: 44.0ms (35.9% of total)...c/correct-round.rkt:119:19: 19.0ms (15.5% of total)backward-pass: 17.0ms (13.9% of total)ival-add: 16.0ms (13% of total)ival-sin: 11.0ms (9% of total)ival-cos: 6.0ms (4.9% of total)ival-div: 5.0ms (4.1% of total)ival-sub: 4.0ms (3.3% of total)const: 1.0ms (0.8% of total)| Inputs |
|---|
#<alt (+ eps 0)> |
#<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 (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 (- (sin (+ x eps)) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))))> |
#<alt (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))> |
#<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 (cos (/ (+ eps (* x 2)) 2))> |
#<alt (* x -1/6)> |
#<alt (* x (* x -1/6))> |
#<alt (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))> |
#<alt (* (* x x) (+ 1/120 (* x (* x -1/5040))))> |
#<alt (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))> |
#<alt (* eps (sin x))> |
| Outputs |
|---|
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 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 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 (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 (* 1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))> |
#<alt (* 1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<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 (* -1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<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 (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 (* -1/6 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 (* -1/6 x)> |
#<alt (* x (- (* 1/120 (pow x 2)) 1/6))> |
#<alt (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* -1/5040 (pow x 5))> |
#<alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 5))> |
#<alt (* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* 1/120 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* -1/5040 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* -1/5040 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* -1/5040 (pow x 6))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 6))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<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))> |
99 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | eps | @ | 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) |
| 1.0ms | eps | @ | inf | (- (sin (+ x eps)) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))) |
| 1× | batch-egg-rewrite |
| 2970× | fma-lowering-fma.f32 |
| 2970× | fma-lowering-fma.f64 |
| 2626× | *-lowering-*.f32 |
| 2626× | *-lowering-*.f64 |
| 1828× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 43 | 187 |
| 1 | 264 | 169 |
| 2 | 2634 | 165 |
| 0 | 8364 | 165 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ eps 0) |
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(sin (/ (+ 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)))) |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))) |
(* x (+ 1 (* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(cos x) |
(* -1/2 (* eps (sin x))) |
(cos (/ (+ eps (* x 2)) 2)) |
(* x -1/6) |
(* x (* x -1/6)) |
(* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(* x (* x (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))) |
(* eps (sin x)) |
| Outputs |
|---|
eps |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
(-.f64 eps #s(literal 0 binary64)) |
(-.f64 eps (/.f64 #s(literal 0 binary64) eps)) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64)) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (neg.f64 (/.f64 #s(literal 0 binary64) eps))) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64)) |
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (neg.f64 (/.f64 #s(literal 0 binary64) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) |
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps eps)) |
(/.f64 (*.f64 eps eps) eps) |
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps)) |
(/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 (*.f64 eps eps))) |
(pow.f64 eps #s(literal 1 binary64)) |
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
(/.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)) |
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(+.f64 x eps) |
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(+.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 |
| 5472× | *-lowering-*.f32 |
| 5472× | *-lowering-*.f64 |
| 2652× | +-lowering-+.f64 |
| 2652× | +-lowering-+.f32 |
| 1638× | neg-lowering-neg.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 421 | 3850 |
| 1 | 1396 | 3373 |
| 2 | 4549 | 3332 |
| 0 | 8884 | 3332 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 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)) |
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))))) |
(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))) |
(* 1/5040 (pow x 7)) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(* 1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* 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))) |
(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)))) |
(* -1/6 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)) |
(* -1/6 x) |
(* x (- (* 1/120 (pow x 2)) 1/6)) |
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* -1/5040 (pow x 5)) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 5)) |
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* 1/120 (pow x 2)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* -1/5040 (pow x 6)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 6)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* 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 |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* 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 (*.f64 eps (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 eps (*.f64 (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 (*.f64 eps (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 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.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 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)))))))))) |
(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))) |
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 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 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 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps 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 x (*.f64 (*.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 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.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 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.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 x (*.f64 (*.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.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))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.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))))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (+ (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 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (sin.f64 x) (-.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 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (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 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (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 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (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 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (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 #s(literal -1/6 binary64) (*.f64 x 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 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)) |
(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 #s(literal 1 binary64) (/.f64 eps x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.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 (+.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 #s(literal 1 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* -1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal -1/6 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)))) |
(* (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 #s(literal -1/6 binary64) (*.f64 x x))) |
(* -1 (* (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)))) |
(* -1 (* (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)))) |
(* -1 (* (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)))) |
(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))))) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal -1/120 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))))) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) |
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (+.f64 (sin.f64 x) (*.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 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (+.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))))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))))))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
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(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
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(* -1/5040 (pow x 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
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(* -1/5040 (pow x 7)) |
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(* eps (cos x)) |
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(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
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(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
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(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
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(* -1/2 (* (pow eps 2) (sin x))) |
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(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
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(*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps))) |
eps |
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(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
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1 |
#s(literal 1 binary64) |
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(cos x) |
(cos.f64 x) |
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1 |
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(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) |
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(cos x) |
(cos.f64 x) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
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(cos (* 1/2 eps)) |
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(* -1/6 (pow x 2)) |
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(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* x (- (* 1/120 (pow x 2)) 1/6)) |
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))))) |
(* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))))) |
(* -1/5040 (pow x 5)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64))) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64))) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))) |
(* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))) |
(* -1/5040 (pow x 5)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 5 binary64))) |
(* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64))) |
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))) |
(* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))) |
(* 1/120 (pow x 2)) |
(*.f64 #s(literal 1/120 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))) |
(* -1/5040 (pow x 4)) |
(*.f64 x (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* -1/5040 (pow x 4)) |
(*.f64 x (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x))) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))))) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))))))) |
(* -1/5040 (pow x 6)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 6 binary64))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(* -1/5040 (pow x 6)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 6 binary64))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x 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 (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 #s(literal -1/6 binary64) (*.f64 x x))))) |
(* 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 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 eps (*.f64 #s(literal -1/5040 binary64) (*.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 20383 to 1913 computations (90.6% saved)
17 alts after pruning (15 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 829 | 12 | 841 |
| Fresh | 4 | 3 | 7 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 837 | 17 | 854 |
| Status | Accuracy | Program |
|---|---|---|
| 37.1% | (-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x)) | |
| 62.9% | (-.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)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 62.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.4% | (+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) | |
| ▶ | 97.6% | (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
| 99.5% | (*.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 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)))))))))) (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 (+.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)) | |
| ▶ | 98.9% | (*.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)) |
| 5.7% | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) | |
| 98.6% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) | |
| ▶ | 98.4% | (*.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 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) | |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) | |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 97.7% | eps |
Compiled 501 to 331 computations (33.9% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 128 | (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 256 | (*.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)) |
| ✓ | cost-diff | 0 | (+.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)))))) |
| ✓ | cost-diff | 0 | (*.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))))))) |
| ✓ | cost-diff | 0 | (+.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)))))))) |
| ✓ | cost-diff | 0 | (*.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))))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps eps) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 eps eps)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps))) |
| ✓ | cost-diff | 0 | (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.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)))))))))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (+.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)))))))))) (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 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)))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 128 | (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
| 2678× | sum3-define |
| 2618× | *-lowering-*.f32 |
| 2618× | *-lowering-*.f64 |
| 1960× | +-lowering-+.f64 |
| 1960× | +-lowering-+.f32 |
Useful iterations: 5 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 359 |
| 1 | 124 | 319 |
| 2 | 392 | 315 |
| 3 | 1202 | 314 |
| 4 | 3411 | 314 |
| 5 | 5423 | 306 |
| 6 | 6423 | 306 |
| 7 | 6710 | 306 |
| 8 | 6748 | 306 |
| 9 | 6803 | 306 |
| 10 | 6916 | 306 |
| 11 | 7343 | 306 |
| 0 | 8336 | 306 |
| 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 (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))) |
-1/48 |
(* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))) |
(* eps (+ 1/3840 (* (* eps eps) -1/645120))) |
(+ 1/3840 (* (* eps eps) -1/645120)) |
1/3840 |
(* (* eps eps) -1/645120) |
(* eps eps) |
-1/645120 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
2 |
eps |
(+ eps (* -1/2 (* x (* eps eps)))) |
eps |
(* -1/2 (* x (* eps eps))) |
-1/2 |
(* x (* eps eps)) |
x |
(* eps eps) |
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))))) |
eps |
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))))) |
1 |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))) |
x |
(+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))) |
(* eps -1/2) |
-1/2 |
(* x (+ -1/2 (* x (* eps 1/12)))) |
(+ -1/2 (* x (* eps 1/12))) |
(* x (* eps 1/12)) |
(* eps 1/12) |
1/12 |
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) |
(* eps 1/2) |
eps |
1/2 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
2 |
| Outputs |
|---|
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (/ (+ eps (* x 2)) 2))) 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)))) |
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (/ (+ eps (* x 2)) 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 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 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 eps (*.f64 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 eps (*.f64 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 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) |
(* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(*.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))))))) |
(+ -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))))) |
(* eps (+ 1/3840 (* (* eps eps) -1/645120))) |
(*.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)) |
(* eps eps) |
(*.f64 eps eps) |
-1/645120 |
#s(literal -1/645120 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(/ (+ eps (* x 2)) 2) |
(+.f64 x (*.f64 eps #s(literal 1/2 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 (* -1/2 (* x (* eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
eps |
(* -1/2 (* x (* eps eps))) |
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
-1/2 |
#s(literal -1/2 binary64) |
(* x (* eps eps)) |
(*.f64 eps (*.f64 eps x)) |
x |
(* eps eps) |
(*.f64 eps eps) |
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))))) |
eps |
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))) |
1 |
#s(literal 1 binary64) |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))) |
(*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))) |
x |
(+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))) |
(+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) |
(* eps -1/2) |
(*.f64 eps #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(* x (+ -1/2 (* x (* eps 1/12)))) |
(*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64))))) |
(+ -1/2 (* x (* eps 1/12))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64)))) |
(* x (* eps 1/12)) |
(*.f64 eps (*.f64 x #s(literal 1/12 binary64))) |
(* eps 1/12) |
(*.f64 eps #s(literal 1/12 binary64)) |
1/12 |
#s(literal 1/12 binary64) |
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 1/2 binary64))) |
(* eps 1/2) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
1/2 |
#s(literal 1/2 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(/ (+ eps (* x 2)) 2) |
(+.f64 x (*.f64 eps #s(literal 1/2 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) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.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)) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (+.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)))))) |
| ✓ | accuracy | 99.8% | (*.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))))))) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
| ✓ | accuracy | 99.5% | (*.f64 eps #s(literal 1/12 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps eps) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps))) |
| ✓ | accuracy | 100.0% | (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 eps eps)) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
| ✓ | accuracy | 99.8% | (*.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)))))))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
| ✓ | accuracy | 99.4% | (*.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))))))) |
| 146.0ms | 254× | 0 | valid |
| 2.0ms | 2× | 1 | valid |
Compiled 395 to 42 computations (89.4% saved)
ival-mult: 35.0ms (52.6% of total)...c/correct-round.rkt:119:19: 16.0ms (24% of total)ival-add: 10.0ms (15% of total)ival-div: 2.0ms (3% of total)ival-cos: 2.0ms (3% of total)const: 1.0ms (1.5% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ (+ eps (* x 2)) 2)> |
#<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 (+ eps (* -1/2 (* x (* eps eps))))> |
#<alt (* -1/2 (* x (* eps eps)))> |
#<alt (* x (* eps eps))> |
#<alt (* eps eps)> |
#<alt (* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))))))> |
#<alt (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))))> |
#<alt (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))))> |
#<alt (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))> |
#<alt (* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (* eps 1/2)> |
#<alt (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))> |
#<alt (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))> |
#<alt (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))))> |
#<alt (* (* eps eps) -1/645120)> |
#<alt (* eps 1/12)> |
#<alt (* x (* eps 1/12))> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
| Outputs |
|---|
#<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 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 (* 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 eps> |
#<alt (* eps (+ 1 (* -1/2 (* eps x))))> |
#<alt (* eps (+ 1 (* -1/2 (* eps x))))> |
#<alt (* eps (+ 1 (* -1/2 (* eps x))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 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 (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))> |
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -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 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))> |
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))> |
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))> |
#<alt (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))> |
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (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 (- (* 1/12 (* eps x)) 1/2)))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))> |
#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))> |
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))> |
#<alt (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1/2 x)> |
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* eps (- (* 1/12 (pow x 2)) 1/2))> |
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))> |
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))> |
#<alt (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))> |
#<alt (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))> |
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))> |
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))> |
#<alt (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))> |
#<alt (* -1/2 eps)> |
#<alt (+ (* -1/2 eps) (* -1/2 x))> |
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))> |
#<alt (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))> |
#<alt (* 1/12 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))> |
#<alt (* 1/12 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))> |
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))> |
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))> |
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))> |
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))> |
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<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 (* -1/48 eps)> |
#<alt (* eps (- (* 1/3840 (pow eps 2)) 1/48))> |
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))> |
#<alt (* -1/645120 (pow eps 5))> |
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))> |
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))> |
#<alt (* -1/645120 (pow eps 5))> |
#<alt (* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))> |
#<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 (* -1/48 (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 (* -1/645120 (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 (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 eps)> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps 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 (* 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))))> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | inf | (+ eps (* -1/2 (* x (* eps eps)))) |
| 4.0ms | x | @ | inf | (* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 2.0ms | x | @ | -inf | (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))) |
| 1.0ms | eps | @ | -inf | (* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1.0ms | eps | @ | 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 |
| 4714× | *-lowering-*.f32 |
| 4714× | *-lowering-*.f64 |
| 2710× | fma-lowering-fma.f32 |
| 2710× | fma-lowering-fma.f64 |
| 2366× | /-lowering-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 246 |
| 1 | 234 | 219 |
| 2 | 2006 | 219 |
| 0 | 8586 | 219 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (+ eps (* x 2)) 2) |
(* (* (* 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 (* x (* eps eps)))) |
(* -1/2 (* x (* eps eps))) |
(* x (* eps eps)) |
(* eps eps) |
(* eps (+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))))) |
(+ 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))))) |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12)))))) |
(+ (* eps -1/2) (* x (+ -1/2 (* x (* eps 1/12))))) |
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) |
(* eps 1/2) |
(* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))) |
(* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))) |
(* (* eps eps) -1/645120) |
(* eps 1/12) |
(* x (* eps 1/12)) |
(cos (/ (+ eps (* x 2)) 2)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64))) |
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) (*.f64 #s(literal 2 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))) |
(/.f64 (*.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (-.f64 eps (*.f64 x #s(literal 2 binary64)))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(*.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(*.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 eps (*.f64 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 (*.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 #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 eps (*.f64 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 #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)))))))) (*.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 (*.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))))))))) (*.f64 #s(literal 2 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 (*.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))))))))) #s(literal 2 binary64))) |
(*.f64 (*.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 eps (*.f64 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 (*.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)))))))))) |
(*.f64 (*.f64 #s(literal 2 binary64) 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 eps (*.f64 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 (*.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)))) |
(+.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 (*.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))))))))) |
(+.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 (*.f64 (*.f64 eps (*.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))))) |
(fma.f64 eps (*.f64 #s(literal 1/2 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 (*.f64 eps (*.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))))))))) |
(fma.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps (*.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))))) |
(fma.f64 #s(literal 1/2 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 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))))))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (*.f64 eps (*.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))))) |
(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 (*.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))))))))) |
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(/.f64 (*.f64 (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) 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))))))) |
(*.f64 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))))))) |
(*.f64 (+.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)))))) eps) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 eps (*.f64 #s(literal -1/645120 binary64) (*.f64 eps (*.f64 eps eps))))) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))) |
(+.f64 (*.f64 (*.f64 eps #s(literal 1/3840 binary64)) eps) (*.f64 (*.f64 #s(literal -1/645120 binary64) (*.f64 eps (*.f64 eps eps))) eps)) |
(+.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (*.f64 eps eps))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (*.f64 eps eps)) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) |
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) (*.f64 eps (*.f64 #s(literal -1/645120 binary64) (*.f64 eps (*.f64 eps eps))))) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (*.f64 eps eps))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) |
(fma.f64 (*.f64 eps eps) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (*.f64 eps eps) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) |
(fma.f64 (*.f64 eps #s(literal 1/3840 binary64)) eps (*.f64 (*.f64 #s(literal -1/645120 binary64) (*.f64 eps (*.f64 eps eps))) eps)) |
(/.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))))) (+.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))) #s(literal 1/3840 binary64))))) |
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/416179814400 binary64)))) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal 1/645120 binary64) (*.f64 eps eps)))) |
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) |
(*.f64 (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))) (*.f64 eps eps)) |
(*.f64 (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) eps) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) |
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(+.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) |
(+.f64 (*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) eps)) |
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(+.f64 (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) |
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) (*.f64 eps (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 eps eps))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))) |
(fma.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) |
(fma.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 eps eps) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) |
(fma.f64 (*.f64 eps #s(literal -1/48 binary64)) eps (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) eps)) |
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(/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))) (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))) (-.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))))))) |
(*.f64 eps (*.f64 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)))))))) |
(*.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))))))) |
(*.f64 (+.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)))))) (*.f64 eps eps)) |
(*.f64 (*.f64 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))))))) 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 #s(literal 1/12 binary64)) |
(*.f64 #s(literal 1/12 binary64) eps) |
(*.f64 eps (*.f64 #s(literal 1/12 binary64) x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(*.f64 #s(literal 1/12 binary64) (*.f64 eps x)) |
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) x) |
(*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) |
(*.f64 (*.f64 x #s(literal 1/12 binary64)) eps) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64))) |
| 1× | egg-herbie |
| 5444× | *-lowering-*.f32 |
| 5444× | *-lowering-*.f64 |
| 2492× | +-lowering-+.f64 |
| 2492× | +-lowering-+.f32 |
| 1610× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 528 | 5468 |
| 1 | 1880 | 4582 |
| 2 | 7053 | 4579 |
| 0 | 8074 | 4579 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
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 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))) |
(* 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))))))) |
eps |
(* eps (+ 1 (* -1/2 (* eps x)))) |
(* eps (+ 1 (* -1/2 (* eps x)))) |
(* eps (+ 1 (* -1/2 (* eps x)))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(* -1/2 (* (pow eps 2) x)) |
(* x (+ (* -1/2 (pow eps 2)) (/ eps x))) |
(* x (+ (* -1/2 (pow eps 2)) (/ eps x))) |
(* x (+ (* -1/2 (pow eps 2)) (/ eps x))) |
(* -1/2 (* (pow eps 2) x)) |
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 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)) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -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 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(* 1/12 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2)))) |
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))) |
(* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3)))))) |
(* 1/12 (* (pow eps 2) (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* 1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x)))) |
(* 1/12 (* eps (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps)))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(* eps (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps)))) |
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))) |
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))) |
(* 1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* 1/12 (* eps (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1/2 x) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(* eps (- (* 1/12 (pow x 2)) 1/2)) |
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2)) |
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2)) |
(* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2)) |
(* -1 (* eps (+ 1/2 (* -1/12 (pow x 2))))) |
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))) |
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))) |
(* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* -1/2 x)) |
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))) |
(+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))) |
(* 1/12 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* 1/12 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 eps))) |
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps)))) |
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps)))))))) |
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps)))))))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x))))))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 eps)))) |
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps)))))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps)))))))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 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) |
(* -1/48 eps) |
(* eps (- (* 1/3840 (pow eps 2)) 1/48)) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* -1/645120 (pow eps 5)) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 5)) |
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(* 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)) |
(* -1/48 (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))))) |
(* -1/645120 (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)) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 eps) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps 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 (* 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)))) |
| Outputs |
|---|
x |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1/2 binary64)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1/2 binary64)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1/2 binary64)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) #s(literal -1 binary64))) |
(* 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 eps (*.f64 (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 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -1/322560 binary64) (pow.f64 eps #s(literal 7 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 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.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 #s(literal 1/2 binary64) eps)))) (+.f64 (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (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 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))) (+.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 eps #s(literal 6 binary64))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 eps #s(literal 4 binary64))))))) |
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -1/322560 binary64) (pow.f64 eps #s(literal 7 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 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #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 #s(literal 1/2 binary64) eps))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)) #s(literal -1/1920 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 #s(literal 1/2 binary64) eps))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)) #s(literal -1/1920 binary64)))) (/.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (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)))))) |
(*.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 #s(literal 1/2 binary64) eps))))) |
(+ (* -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 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 #s(literal 1/2 binary64) eps))))) (*.f64 (*.f64 (*.f64 eps #s(literal -2 binary64)) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) 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)))))))))) |
(+ (* 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 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 #s(literal 1/2 binary64) eps))))) (*.f64 x (-.f64 (*.f64 (*.f64 eps (sin.f64 (*.f64 #s(literal 1/2 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)))))))) #s(literal -2 binary64))) (*.f64 x (*.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 #s(literal 1/2 binary64) eps)))))))) |
(+ (* 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 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 #s(literal 1/2 binary64) eps))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps (sin.f64 (*.f64 #s(literal 1/2 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)))))))) #s(literal -2 binary64))) (*.f64 x (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) 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 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 #s(literal 1/2 binary64) eps))))))))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
(* 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)))))) |
(*.f64 eps (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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))) |
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(* 1/2 (* eps (cos x))) |
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(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 x (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps)))))))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps #s(literal -1/4 binary64))))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps)))))))))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps #s(literal -1/4 binary64))) (*.f64 (*.f64 x (*.f64 eps #s(literal 1/12 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* -1/48 eps) |
(*.f64 eps #s(literal -1/48 binary64)) |
(* eps (- (* 1/3840 (pow eps 2)) 1/48)) |
(*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(*.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)))))) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(*.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)))))) |
(* -1/645120 (pow eps 5)) |
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(*.f64 (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64))) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))) (pow.f64 eps #s(literal 5 binary64))) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))) (pow.f64 eps #s(literal 5 binary64))) |
(* -1/645120 (pow eps 5)) |
(*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (+.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal -1/3840 binary64) (*.f64 eps eps))) (neg.f64 (pow.f64 eps #s(literal 5 binary64)))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (+.f64 #s(literal 1/645120 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -1/3840 binary64) (*.f64 eps eps)))) (neg.f64 (pow.f64 eps #s(literal 5 binary64)))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(*.f64 (+.f64 #s(literal 1/645120 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -1/3840 binary64) (*.f64 eps eps)))) (neg.f64 (pow.f64 eps #s(literal 5 binary64)))) |
(* 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 (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 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)))) |
(* -1/48 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(*.f64 (*.f64 eps 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 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))))))) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(*.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))))))) |
(* -1/645120 (pow eps 6)) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 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) (pow.f64 eps #s(literal 4 binary64)))))) |
(* (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) (pow.f64 eps #s(literal 4 binary64)))))) |
(* -1/645120 (pow eps 6)) |
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 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) (pow.f64 eps #s(literal 4 binary64)))))) |
(* (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) (pow.f64 eps #s(literal 4 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)) |
(* -1/645120 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 eps) |
(*.f64 eps #s(literal 1/12 binary64)) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(* 1/12 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal 1/12 binary64))) |
(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 eps (*.f64 (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 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+ (cos (* 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 #s(literal 1/2 binary64) eps)) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
Compiled 23194 to 2100 computations (90.9% saved)
22 alts after pruning (18 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 824 | 10 | 834 |
| Fresh | 2 | 8 | 10 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 2 | 2 |
| Total | 829 | 22 | 851 |
| Status | Accuracy | Program |
|---|---|---|
| 98.4% | (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) | |
| 37.1% | (-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x)) | |
| 62.9% | (-.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)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 62.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.4% | (+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) | |
| 52.1% | (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 eps (*.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))))))) (*.f64 (*.f64 eps (*.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))))))))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps (*.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)) | |
| ▶ | 99.5% | (*.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)) |
| 53.4% | (*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) #s(literal 2 binary64)) | |
| ▶ | 99.5% | (*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
| 99.3% | (*.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)) | |
| ▶ | 5.7% | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
| ▶ | 98.4% | (*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
| 98.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) | |
| 98.4% | (*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) | |
| ✓ | 98.4% | (*.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))))))))) |
| 98.3% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) | |
| ▶ | 97.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) | |
| 98.9% | (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) | |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 97.7% | eps |
Compiled 1033 to 541 computations (47.6% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.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))))) |
| ✓ | 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) #s(literal 1/3840 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) #s(literal 1/3840 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) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
| ✓ | cost-diff | 128 | (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
| ✓ | cost-diff | 0 | (+.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))))))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.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)))))))))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
| 3080× | *-lowering-*.f32 |
| 3080× | *-lowering-*.f64 |
| 1926× | +-lowering-+.f64 |
| 1926× | +-lowering-+.f32 |
| 1686× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 675 |
| 1 | 205 | 541 |
| 2 | 675 | 524 |
| 3 | 2542 | 524 |
| 4 | 4850 | 524 |
| 0 | 8022 | 524 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps)))) 2) |
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps)))) |
(* 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 (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))) |
-1/48 |
(* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))) |
(* eps (+ 1/3840 (* (* eps eps) -1/645120))) |
(+ 1/3840 (* (* eps eps) -1/645120)) |
1/3840 |
(* (* eps eps) -1/645120) |
(* eps eps) |
-1/645120 |
(cos (+ x (* 1/2 eps))) |
(+ x (* 1/2 eps)) |
x |
(* 1/2 eps) |
2 |
(* x (* (* x x) 1/6)) |
x |
(* (* x x) 1/6) |
(* x x) |
1/6 |
(* eps (+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120))))))) |
eps |
(+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120)))))) |
1 |
(* eps (* eps (+ -1/6 (* eps (* eps 1/120))))) |
(* eps (+ -1/6 (* eps (* eps 1/120)))) |
(+ -1/6 (* eps (* eps 1/120))) |
-1/6 |
(* eps (* eps 1/120)) |
(* eps 1/120) |
1/120 |
(* eps (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))))) |
eps |
(/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))) |
1 |
(/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))) |
(- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))) |
x |
(+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) |
(* eps -1/2) |
-1/2 |
(* x (+ -1/2 (* eps (* 1/12 x)))) |
(+ -1/2 (* eps (* 1/12 x))) |
(* eps (* 1/12 x)) |
(* 1/12 x) |
1/12 |
(- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))) |
(* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))) |
(* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) |
eps |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) |
1/2 |
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))) |
(* eps eps) |
(+ -1/48 (* (* eps eps) 1/3840)) |
-1/48 |
(* (* eps eps) 1/3840) |
1/3840 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
2 |
| Outputs |
|---|
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps)))) 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 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) |
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 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 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 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 (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(*.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)))))) |
(+ -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)))) |
(* eps (+ 1/3840 (* (* eps eps) -1/645120))) |
(*.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)) |
(* eps eps) |
(*.f64 eps eps) |
-1/645120 |
#s(literal -1/645120 binary64) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(+ x (* 1/2 eps)) |
(+.f64 x (*.f64 eps #s(literal 1/2 binary64))) |
x |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
2 |
#s(literal 2 binary64) |
(* x (* (* x x) 1/6)) |
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))) |
x |
(* (* x x) 1/6) |
(*.f64 x (*.f64 x #s(literal 1/6 binary64))) |
(* x x) |
(*.f64 x x) |
1/6 |
#s(literal 1/6 binary64) |
(* eps (+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))))) |
eps |
(+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120)))))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))) |
1 |
#s(literal 1 binary64) |
(* eps (* eps (+ -1/6 (* eps (* eps 1/120))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))) |
(* eps (+ -1/6 (* eps (* eps 1/120)))) |
(*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))) |
(+ -1/6 (* eps (* eps 1/120))) |
(+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))) |
-1/6 |
#s(literal -1/6 binary64) |
(* eps (* eps 1/120)) |
(*.f64 eps (*.f64 eps #s(literal 1/120 binary64))) |
(* eps 1/120) |
(*.f64 eps #s(literal 1/120 binary64)) |
1/120 |
#s(literal 1/120 binary64) |
(* eps (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))))) |
(/.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))))))) |
eps |
(/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))))) |
1 |
#s(literal 1 binary64) |
(/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))))))) |
(- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))) |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))) |
(*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))) |
x |
(+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) |
(+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) |
(* eps -1/2) |
(*.f64 eps #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(* x (+ -1/2 (* eps (* 1/12 x)))) |
(*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64))))) |
(+ -1/2 (* eps (* 1/12 x))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64)))) |
(* eps (* 1/12 x)) |
(*.f64 eps (*.f64 x #s(literal 1/12 binary64))) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
1/12 |
#s(literal 1/12 binary64) |
(- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))) |
(-.f64 #s(literal 1 binary64) (*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))))) |
(* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))) |
(*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64))))))))) |
(* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/12 binary64)))))))) |
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))))) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))) (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))))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))) |
eps |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))) |
1/2 |
#s(literal 1/2 binary64) |
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) |
(* eps eps) |
(*.f64 eps eps) |
(+ -1/48 (* (* eps eps) 1/3840)) |
(+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))) |
-1/48 |
#s(literal -1/48 binary64) |
(* (* eps eps) 1/3840) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
1/3840 |
#s(literal 1/3840 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) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.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)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.8% | (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) |
| ✓ | accuracy | 99.8% | (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)) |
| ✓ | accuracy | 99.8% | (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))) |
| ✓ | accuracy | 99.5% | (*.f64 #s(literal 1/12 binary64) x) |
| ✓ | accuracy | 99.9% | (*.f64 eps #s(literal 1/120 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))) |
| ✓ | accuracy | 99.4% | (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64))))) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) |
| ✓ | accuracy | 99.8% | (*.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)))))))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))) |
| ✓ | accuracy | 99.4% | (*.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))))))) |
| 252.0ms | 254× | 0 | valid |
| 3.0ms | 2× | 1 | valid |
Compiled 748 to 64 computations (91.4% saved)
ival-mult: 85.0ms (60.9% of total)...c/correct-round.rkt:119:19: 27.0ms (19.3% of total)ival-add: 14.0ms (10% of total)ival-cos: 6.0ms (4.3% of total)ival-div: 5.0ms (3.6% of total)ival-sub: 2.0ms (1.4% of total)const: 1.0ms (0.7% 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 (+ x (* 1/2 eps)))) 2)> |
#<alt (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps))))> |
#<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 (* x (* (* x x) 1/6))> |
#<alt (* (* x x) 1/6)> |
#<alt (* x x)> |
#<alt (* eps (+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120)))))))> |
#<alt (+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120))))))> |
#<alt (* eps (* eps (+ -1/6 (* eps (* eps 1/120)))))> |
#<alt (* eps (+ -1/6 (* eps (* eps 1/120))))> |
#<alt (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))))> |
#<alt (* eps (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))))> |
#<alt (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))> |
#<alt (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))> |
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))))> |
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))> |
#<alt (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))> |
#<alt (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))> |
#<alt (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))))> |
#<alt (* (* eps eps) -1/645120)> |
#<alt (* eps (* eps 1/120))> |
#<alt (* eps 1/120)> |
#<alt (* 1/12 x)> |
#<alt (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))> |
#<alt (* eps (* 1/12 x))> |
#<alt (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))> |
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))> |
#<alt (* (* eps eps) 1/3840)> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
| 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 (+ 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 (* 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 (* 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 (+ x (* 1/2 eps)))))> |
#<alt (* (pow eps 7) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 7) (+ (* -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 7) (+ (* -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 7) (cos (- x (* -1/2 eps)))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/645120 (cos (- x (* -1/2 eps)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/645120 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4)))))))> |
#<alt (* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 6))) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/645120 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 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 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))> |
#<alt (* 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 (- (* 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 (- (* 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 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 (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* 1/6 (pow x 3))> |
#<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 (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<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) (- (* 1/120 (pow eps 2)) 1/6))))> |
#<alt (* 1/120 (pow eps 5))> |
#<alt (* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* 1/120 (pow eps 5))> |
#<alt (* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))> |
#<alt (* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))> |
#<alt (* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))> |
#<alt 1> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))> |
#<alt (* 1/120 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* 1/120 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* 1/120 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* 1/120 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1/6 eps)> |
#<alt (* eps (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* eps (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* eps (- (* 1/120 (pow eps 2)) 1/6))> |
#<alt (* 1/120 (pow eps 3))> |
#<alt (* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* 1/120 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))> |
#<alt (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))> |
#<alt (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (- (* -1/2 x) (* 1/2 eps))))> |
#<alt (+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 3) (- (+ (* 1/12 eps) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* eps (pow x 2))))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 3 (/ 1 (* eps (pow x 2))))))))> |
#<alt (* (pow x 3) (- (+ (* 1/12 eps) (+ (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* eps (pow x 2)))) (* 4 (/ 1 (pow x 3))))) (+ (* -6 (/ (- (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (+ (* -1/2 eps) (* 3 (/ 1 eps)))) (* eps (pow x 3)))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 3 (/ 1 (* eps (pow x 2)))))))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (* 3 (/ 1 eps))) (* 1/2 eps)) x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (+ (* -1 (/ (- 4 (* 6 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (* 3 (/ 1 eps))) (* 1/2 eps)) eps))) x)) (* 3 (/ 1 eps)))) (* 1/2 eps)) x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (/ (- 1 (* 1/4 (pow x 4))) (- 1 (* -1/2 (pow x 2))))> |
#<alt (- (+ (* eps (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))> |
#<alt (- (+ (* eps (- (+ (* eps (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))> |
#<alt (- (+ (* eps (- (+ (* eps (- (+ (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (/ (* eps (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2)))))) (- (* 1/12 (pow x 2)) 1/2)))) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))> |
#<alt (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* eps (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))> |
#<alt (* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))))> |
#<alt (* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))))> |
#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps)) (* -1 (pow x 2))) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps)) (* -1 (pow x 2))) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (/ (* eps (- 1 (* 1/4 (pow x 4)))) (- 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (- (+ (* eps (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))))> |
#<alt (* eps (- (+ (* eps (- (+ (* eps (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))))> |
#<alt (* eps (- (+ (* eps (- (+ (* eps (- (+ (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (/ (* eps (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2)))))) (- (* 1/12 (pow x 2)) 1/2)))) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))))> |
#<alt (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))))> |
#<alt (* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (pow x 2) eps))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (+ (* -1 (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps))) 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 (- (* x (- (* 1/12 (* (pow eps 2) x)) (* 1/2 eps))) (* 1/2 (pow eps 2)))))> |
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))> |
#<alt (* (pow x 3) (- (+ (* -1 (/ eps x)) (* 1/12 (pow eps 2))) (* -1/2 (/ eps x))))> |
#<alt (* (pow x 3) (- (+ (* -1 (/ eps x)) (+ (* 1/12 (pow eps 2)) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow x 2))))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (* eps (pow x 2)))) (+ (* -1/2 (/ eps x)) (* -1/2 (/ (pow eps 2) (pow x 2)))))))> |
#<alt (* (pow x 3) (- (+ (* -1 (/ eps x)) (+ (* 1/12 (pow eps 2)) (+ (* 6 (/ eps (pow x 3))) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow x 2)))))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (* eps (pow x 2)))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (pow x 3))) (+ (* -6 (/ (- (* 12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) eps)) (* -1/2 (pow eps 2)))) (* eps (pow x 3)))) (+ (* -1 (/ eps (pow x 3))) (+ (* -1/2 (/ eps x)) (* -1/2 (/ (pow eps 2) (pow x 2))))))))))> |
#<alt (* 1/12 (* (pow eps 2) (pow x 3)))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 eps) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 eps) (* -1 (/ (- (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) x))) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 eps) (* -1 (/ (- (+ (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (* -1 (/ (- (* 6 eps) (+ (* -6 (- (* -1 eps) (* -1/2 eps))) (+ (* -1 eps) (* 6 (/ (- (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) eps))))) x))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) x))) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* 1/2 eps) (* x (- 1/2 (* -1/4 (pow eps 2)))))))> |
#<alt (+ 1 (* x (+ (* 1/2 eps) (* x (- (+ 1/2 (* x (- (* -1/12 eps) (+ (* -1/2 eps) (* -1/8 (pow eps 3)))))) (* -1/4 (pow eps 2)))))))> |
#<alt (/ 12 (* eps (pow x 3)))> |
#<alt (/ (+ (* 12 (/ 1 eps)) (* 72 (/ 1 (* (pow eps 2) x)))) (pow x 3))> |
#<alt (/ (- (+ (* 12 (/ 1 eps)) (+ (* 864 (/ 1 (* (pow eps 3) (pow x 2)))) (/ 72 (* (pow eps 2) x)))) (+ (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 3) (pow x 2)))) (* 72 (/ 1 (* eps (pow x 2)))))) (pow x 3))> |
#<alt (/ (- (+ (* -1 (/ (+ (* -12 (/ (- (* 864 (/ 1 (pow eps 3))) (+ (* 72 (/ 1 eps)) (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))))) eps)) (+ (* 144 (/ 1 (pow eps 2))) (+ (* 864 (/ 1 (pow eps 2))) (* 10368 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 4)))))) (pow x 3))) (+ (* 12 (/ 1 eps)) (+ (* 864 (/ 1 (* (pow eps 3) (pow x 2)))) (/ 72 (* (pow eps 2) x))))) (+ (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 3) (pow x 2)))) (* 72 (/ 1 (* eps (pow x 2)))))) (pow x 3))> |
#<alt (/ 12 (* eps (pow x 3)))> |
#<alt (/ (+ (* 12 (/ 1 eps)) (* 72 (/ 1 (* (pow eps 2) x)))) (pow x 3))> |
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 72 (/ 1 eps)) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) x)) (* 72 (/ 1 (pow eps 2)))) x)) (* 12 (/ 1 eps))) (pow x 3)))> |
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* 12 (/ (- (* 72 (/ 1 eps)) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) (* eps x))) (+ (* 72 (/ 1 eps)) (+ (* 10368 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 4) x))) (+ (/ 144 (* (pow eps 2) x)) (/ 864 (* (pow eps 2) x)))))) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) x)) (* 72 (/ 1 (pow eps 2)))) x)) (* 12 (/ 1 eps))) (pow x 3)))> |
#<alt (/ (- 1 (* -1/2 (pow x 2))) (- 1 (* 1/4 (pow x 4))))> |
#<alt (- (+ (* eps (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4))))))> |
#<alt (- (+ (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4))))))) (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4)))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4))))))> |
#<alt (- (+ (* eps (- (+ (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow x 2) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (- 1 (* 1/4 (pow x 4))))) (* -1 (/ (* (pow x 3) (* (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4))))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4)))))))) (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4)))))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4))))))> |
#<alt (/ 1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2))))) eps)> |
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3))))) (pow eps 2))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2)))))) eps)> |
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (- 1 (* 1/4 (pow x 4)))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ (* x (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3)))))) (- (* 1/12 (pow x 2)) 1/2))) (pow eps 3))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2)))))) (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3))))))) eps)> |
#<alt (/ -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (* eps (+ 1/2 (* -1/12 (pow x 2)))))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* eps (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3))))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps))> |
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))) (- 1 (* 1/4 (pow x 4)))) (* eps (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2))))) (/ (* x (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3)))))) (* eps (+ 1/2 (* -1/12 (pow x 2)))))) (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3)))))) eps)) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps))> |
#<alt 1> |
#<alt (+ 1 (* 1/2 (* eps x)))> |
#<alt (+ 1 (* x (- (* 1/2 x) (* -1/2 eps))))> |
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/12 (* eps x)))) (* -1/2 eps))))> |
#<alt (* -1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (* 1/12 eps)))> |
#<alt (* (pow x 3) (- (+ (* 1/2 (/ eps (pow x 2))) (* 1/2 (/ 1 x))) (* 1/12 eps)))> |
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps))))> |
#<alt (* -1/12 (* eps (pow x 3)))> |
#<alt (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (* 1/2 (/ eps x)) (/ 1 (pow x 2)))) x)) (* -1/12 eps))))> |
#<alt (- 1 (* -1/2 (pow x 2)))> |
#<alt (- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2)))> |
#<alt (- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2)))> |
#<alt (- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2)))> |
#<alt (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))> |
#<alt (* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))))> |
#<alt (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))> |
#<alt (* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<alt (* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
#<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 (* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))> |
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))> |
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#<alt (* 1/120 (pow eps 2))> |
#<alt (* 1/120 (pow eps 2))> |
#<alt (* 1/120 (pow eps 2))> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/120 eps)> |
#<alt (* 1/12 x)> |
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#<alt (* 1/12 x)> |
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#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
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#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
#<alt (* 1/12 x)> |
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#<alt (* 1/12 (* eps (pow x 3)))> |
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#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))> |
#<alt (* -1/2 (pow x 2))> |
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#<alt (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))> |
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#<alt (* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))> |
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#<alt (* 1/12 (* eps x))> |
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#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/12 (* eps x))> |
#<alt (* 1/4 (pow x 3))> |
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#<alt (+ (* 1/4 (pow x 3)) (* eps (+ (* -1 (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2))) (* eps (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2))))))> |
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#<alt (* (pow eps 2) (+ (* -1 (/ (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)) eps)) (+ (* 1/4 (/ (pow x 3) (pow eps 2))) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2)))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)) eps)) (+ (* 1/4 (/ (pow x 3) (pow eps 2))) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2)))))> |
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#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* (pow x 2) (+ 1/2 (* -1/12 (pow x 2))))) (* -1/4 (/ (pow x 3) eps))) eps)) (* x (pow (+ 1/2 (* -1/12 (pow x 2))) 2))))> |
#<alt (* 1/4 (* (pow eps 2) x))> |
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#<alt (* (pow x 5) (+ (* -1/12 (/ eps x)) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/144 (pow eps 2)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1/4 (pow x 2)))))))> |
#<alt (* 1/144 (* (pow eps 2) (pow x 5)))> |
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#<alt (* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ 1/4 (* -1/12 (pow eps 2)))) (* -1/2 (/ eps x))) x)) (* -1/12 eps)) x)) (* -1/144 (pow eps 2)))))> |
#<alt (* -1/48 (pow eps 2))> |
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#<alt (* 1/3840 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* 1/3840 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (* 1/3840 (pow eps 2))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (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))))> |
132 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | x | @ | -inf | (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 4.0ms | x | @ | 0 | (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) |
| 2.0ms | x | @ | inf | (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))) |
| 2.0ms | eps | @ | 0 | (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))) |
| 2.0ms | eps | @ | 0 | (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))) |
| 1× | batch-egg-rewrite |
| 4028× | *-lowering-*.f32 |
| 4028× | *-lowering-*.f64 |
| 2306× | /-lowering-/.f32 |
| 2306× | /-lowering-/.f64 |
| 1680× | pow-lowering-pow.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 489 |
| 1 | 394 | 348 |
| 2 | 3416 | 336 |
| 0 | 8666 | 336 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps)))) 2) |
(* (* eps (+ 1/2 (* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))))) (cos (+ x (* 1/2 eps)))) |
(* 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)))))))) |
(* x (* (* x x) 1/6)) |
(* (* x x) 1/6) |
(* x x) |
(* eps (+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120))))))) |
(+ 1 (* eps (* eps (+ -1/6 (* eps (* eps 1/120)))))) |
(* eps (* eps (+ -1/6 (* eps (* eps 1/120))))) |
(* eps (+ -1/6 (* eps (* eps 1/120)))) |
(/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))))))) |
(* eps (/ 1 (/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))))) |
(/ (- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) (- 1 (* x (* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))))))) |
(- 1 (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))))) |
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840)))) |
(* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))))) |
(* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120)))) |
(* eps (* eps (+ -1/48 (* eps (* eps (+ 1/3840 (* (* eps eps) -1/645120))))))) |
(* (* eps eps) -1/645120) |
(* eps (* eps 1/120)) |
(* eps 1/120) |
(* 1/12 x) |
(* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x)))))) |
(* eps (* 1/12 x)) |
(* (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))) (* x (+ (* eps -1/2) (* x (+ -1/2 (* eps (* 1/12 x))))))) |
(* (* eps eps) (+ -1/48 (* (* eps eps) 1/3840))) |
(* (* eps eps) 1/3840) |
(cos (/ (+ eps (* x 2)) 2)) |
| Outputs |
|---|
(*.f64 eps (*.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)))) #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 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps 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 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 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 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)))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps (+.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)))))))))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 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 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 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 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 eps 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 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (*.f64 (*.f64 eps 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)))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(*.f64 eps (*.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))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 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 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.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 (*.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))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) eps) |
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) eps) (+.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 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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 eps 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 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 eps 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 #s(literal 1/2 binary64) eps (*.f64 (*.f64 eps 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 1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps 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 eps eps) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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 eps (+.f64 #s(literal 1/8 binary64) (*.f64 (*.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 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 eps 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 #s(literal 1/4 binary64) (*.f64 (*.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 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)))))))) #s(literal 1/2 binary64))))) |
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(/.f64 (*.f64 (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) |
(/.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 eps #s(literal -1/2 binary64)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))))) (neg.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 eps #s(literal -1/2 binary64))))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))))) (neg.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))))) (neg.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (-.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))) (*.f64 eps #s(literal -1/2 binary64))))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))))) (neg.f64 (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) |
(*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) |
(*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))))) |
(*.f64 (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) |
(*.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64))))) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))) x) |
(+.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) |
(+.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64)))) (+.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (-.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) |
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64))))) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))) |
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/2304 binary64) (*.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) (-.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) |
(/.f64 (*.f64 (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64)))) (*.f64 eps eps)) (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/2304 binary64) (*.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (*.f64 eps eps)) (-.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) |
(/.f64 (neg.f64 (+.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64))) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64))))) (neg.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))) (neg.f64 (-.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/2304 binary64) (*.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))))) (neg.f64 (-.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal -1/110592 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/56623104000 binary64)))) (*.f64 eps eps))) (neg.f64 (+.f64 #s(literal 1/2304 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) #s(literal -1/48 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/2304 binary64) (*.f64 #s(literal 1/14745600 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) |
(*.f64 (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))) (*.f64 eps eps)) |
(*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))) eps) |
(*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(*.f64 (*.f64 eps #s(literal 1/3840 binary64)) eps) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64))) |
| 1× | egg-herbie |
| 6492× | *-lowering-*.f32 |
| 6492× | *-lowering-*.f64 |
| 3952× | +-lowering-+.f64 |
| 3952× | +-lowering-+.f32 |
| 1768× | /-lowering-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1166 | 11310 |
| 1 | 4319 | 9918 |
| 0 | 9373 | 9918 |
| 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 (+ 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)))))))) |
(* 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)))))) |
(* 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 (+ x (* 1/2 eps))))) |
(* (pow eps 7) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 7) (+ (* -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 7) (+ (* -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 7) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/645120 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/645120 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))))))) |
(* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 6))) (+ (* -1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/645120 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (cos (+ x (* 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 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* 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 (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) |
(* eps (* (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 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))))) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 1/6 (pow x 3)) |
(* 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)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
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) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* 1/120 (pow eps 5)) |
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* 1/120 (pow eps 5)) |
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120))) |
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4)))))) |
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4)))))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))) |
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))) |
(* 1/120 (pow eps 4)) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* 1/120 (pow eps 4)) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2))))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)) |
(* 1/120 (pow eps 4)) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* 1/120 (pow eps 4)) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* -1/6 eps) |
(* eps (- (* 1/120 (pow eps 2)) 1/6)) |
(* eps (- (* 1/120 (pow eps 2)) 1/6)) |
(* eps (- (* 1/120 (pow eps 2)) 1/6)) |
(* 1/120 (pow eps 3)) |
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2))))) |
(* 1/120 (pow eps 3)) |
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120))) |
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120))) |
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (- (* -1/2 x) (* 1/2 eps)))) |
(+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps)))) |
(* 1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* 1/12 eps) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* eps (pow x 2))))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 3 (/ 1 (* eps (pow x 2)))))))) |
(* (pow x 3) (- (+ (* 1/12 eps) (+ (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* eps (pow x 2)))) (* 4 (/ 1 (pow x 3))))) (+ (* -6 (/ (- (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (+ (* -1/2 eps) (* 3 (/ 1 eps)))) (* eps (pow x 3)))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 3 (/ 1 (* eps (pow x 2))))))))) |
(* 1/12 (* eps (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (* 3 (/ 1 eps))) (* 1/2 eps)) x)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (+ (* -1 (/ (- 4 (* 6 (/ (- (+ (* -12 (/ (+ 1/4 (* -1/12 (pow eps 2))) eps)) (* 3 (/ 1 eps))) (* 1/2 eps)) eps))) x)) (* 3 (/ 1 eps)))) (* 1/2 eps)) x)) 1/2) x)) (* -1/12 eps)))) |
(/ (- 1 (* 1/4 (pow x 4))) (- 1 (* -1/2 (pow x 2)))) |
(- (+ (* eps (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))) |
(- (+ (* eps (- (+ (* eps (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))) |
(- (+ (* eps (- (+ (* eps (- (+ (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (/ (* eps (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2)))))) (- (* 1/12 (pow x 2)) 1/2)))) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2)))))) |
(* eps (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* eps (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
(* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
(* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* -1 (* eps (+ (* -1 (/ (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps)) (* -1 (pow x 2))) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps)) (* -1 (pow x 2))) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(/ (* eps (- 1 (* 1/4 (pow x 4)))) (- 1 (* -1/2 (pow x 2)))) |
(* eps (- (+ (* eps (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
(* eps (- (+ (* eps (- (+ (* eps (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
(* eps (- (+ (* eps (- (+ (* eps (- (+ (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (/ (* eps (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2)))))) (- (* 1/12 (pow x 2)) 1/2)))) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* (pow eps 2) (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
(* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
(* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
(* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* (pow eps 2) (- (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (pow x 2) eps))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) eps)))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (+ (* -1 (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps))) eps)))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (- (* -1/2 (* eps x)) (* 1/2 (pow eps 2))))) |
(+ eps (* x (- (* x (- (* 1/12 (* (pow eps 2) x)) (* 1/2 eps))) (* 1/2 (pow eps 2))))) |
(* 1/12 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (- (+ (* -1 (/ eps x)) (* 1/12 (pow eps 2))) (* -1/2 (/ eps x)))) |
(* (pow x 3) (- (+ (* -1 (/ eps x)) (+ (* 1/12 (pow eps 2)) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow x 2))))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (* eps (pow x 2)))) (+ (* -1/2 (/ eps x)) (* -1/2 (/ (pow eps 2) (pow x 2))))))) |
(* (pow x 3) (- (+ (* -1 (/ eps x)) (+ (* 1/12 (pow eps 2)) (+ (* 6 (/ eps (pow x 3))) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow x 2)))))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (* eps (pow x 2)))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (pow x 3))) (+ (* -6 (/ (- (* 12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) eps)) (* -1/2 (pow eps 2)))) (* eps (pow x 3)))) (+ (* -1 (/ eps (pow x 3))) (+ (* -1/2 (/ eps x)) (* -1/2 (/ (pow eps 2) (pow x 2)))))))))) |
(* 1/12 (* (pow eps 2) (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 eps) (* -1/2 eps)) x)) (* -1/12 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 eps) (* -1 (/ (- (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) x))) (* -1/2 eps)) x)) (* -1/12 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 eps) (* -1 (/ (- (+ (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (* -1 (/ (- (* 6 eps) (+ (* -6 (- (* -1 eps) (* -1/2 eps))) (+ (* -1 eps) (* 6 (/ (- (* -12 (+ 1/4 (* -1/12 (pow eps 2)))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) eps))))) x))) (+ (* 1/2 (pow eps 2)) (* 6 (/ (- (* -1 eps) (* -1/2 eps)) eps)))) x))) (* -1/2 eps)) x)) (* -1/12 (pow eps 2))))) |
1 |
(+ 1 (* 1/2 (* eps x))) |
(+ 1 (* x (+ (* 1/2 eps) (* x (- 1/2 (* -1/4 (pow eps 2))))))) |
(+ 1 (* x (+ (* 1/2 eps) (* x (- (+ 1/2 (* x (- (* -1/12 eps) (+ (* -1/2 eps) (* -1/8 (pow eps 3)))))) (* -1/4 (pow eps 2))))))) |
(/ 12 (* eps (pow x 3))) |
(/ (+ (* 12 (/ 1 eps)) (* 72 (/ 1 (* (pow eps 2) x)))) (pow x 3)) |
(/ (- (+ (* 12 (/ 1 eps)) (+ (* 864 (/ 1 (* (pow eps 3) (pow x 2)))) (/ 72 (* (pow eps 2) x)))) (+ (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 3) (pow x 2)))) (* 72 (/ 1 (* eps (pow x 2)))))) (pow x 3)) |
(/ (- (+ (* -1 (/ (+ (* -12 (/ (- (* 864 (/ 1 (pow eps 3))) (+ (* 72 (/ 1 eps)) (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))))) eps)) (+ (* 144 (/ 1 (pow eps 2))) (+ (* 864 (/ 1 (pow eps 2))) (* 10368 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 4)))))) (pow x 3))) (+ (* 12 (/ 1 eps)) (+ (* 864 (/ 1 (* (pow eps 3) (pow x 2)))) (/ 72 (* (pow eps 2) x))))) (+ (* 1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 3) (pow x 2)))) (* 72 (/ 1 (* eps (pow x 2)))))) (pow x 3)) |
(/ 12 (* eps (pow x 3))) |
(/ (+ (* 12 (/ 1 eps)) (* 72 (/ 1 (* (pow eps 2) x)))) (pow x 3)) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 72 (/ 1 eps)) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) x)) (* 72 (/ 1 (pow eps 2)))) x)) (* 12 (/ 1 eps))) (pow x 3))) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* 12 (/ (- (* 72 (/ 1 eps)) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) (* eps x))) (+ (* 72 (/ 1 eps)) (+ (* 10368 (/ (+ 1/4 (* -1/12 (pow eps 2))) (* (pow eps 4) x))) (+ (/ 144 (* (pow eps 2) x)) (/ 864 (* (pow eps 2) x)))))) (+ (* -1728 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow eps 3))) (* 864 (/ 1 (pow eps 3))))) x)) (* 72 (/ 1 (pow eps 2)))) x)) (* 12 (/ 1 eps))) (pow x 3))) |
(/ (- 1 (* -1/2 (pow x 2))) (- 1 (* 1/4 (pow x 4)))) |
(- (+ (* eps (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4)))))) |
(- (+ (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4))))))) (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4)))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4)))))) |
(- (+ (* eps (- (+ (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow x 2) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (- 1 (* 1/4 (pow x 4))))) (* -1 (/ (* (pow x 3) (* (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4))))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4)))))))) (+ (* -1 (/ (* (pow x 2) (* (- 1 (* -1/2 (pow x 2))) (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (/ (* (pow x 3) (* (- (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* 1/4 (pow x 4))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2))) (- (* 1/12 (pow x 2)) 1/2))) (- 1 (* 1/4 (pow x 4)))))))) (/ (* (pow x 3) (* (- 1 (* -1/2 (pow x 2))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* 1/4 (pow x 4))) 2)))) (/ 1 (- 1 (* 1/4 (pow x 4))))) (* -1/2 (/ (pow x 2) (- 1 (* 1/4 (pow x 4)))))) |
(/ 1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2))))) eps) |
(/ (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3))))) (pow eps 2))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2)))))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (- 1 (* 1/4 (pow x 4)))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ (* x (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3)))))) (- (* 1/12 (pow x 2)) 1/2))) (pow eps 3))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* eps (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) (+ (/ 1 (* eps (pow (- (* 1/12 (pow x 2)) 1/2) 2))) (/ 1 (* x (- (* 1/12 (pow x 2)) 1/2)))))) (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (/ 1 (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* (pow x 3) (pow (- (* 1/12 (pow x 2)) 1/2) 3))))))) eps) |
(/ -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (* eps (+ 1/2 (* -1/12 (pow x 2)))))) (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* eps (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3))))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps)) |
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ (* -1 (/ (- (+ (* -1 (/ (* (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2))) (- 1 (* 1/4 (pow x 4)))) (* eps (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2))))) (/ (* x (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3)))))) (* eps (+ 1/2 (* -1/12 (pow x 2)))))) (+ (* -1 (/ (* x (+ (* -1 (/ (- 1 (* -1/2 (pow x 2))) (* (pow x 2) (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow x 3) (pow (+ 1/2 (* -1/12 (pow x 2))) 3)))))) eps)) (/ 1 (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) eps)) (/ 1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps)) |
1 |
(+ 1 (* 1/2 (* eps x))) |
(+ 1 (* x (- (* 1/2 x) (* -1/2 eps)))) |
(+ 1 (* x (- (* x (+ 1/2 (* -1/12 (* eps x)))) (* -1/2 eps)))) |
(* -1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (* 1/2 (/ 1 x)) (* 1/12 eps))) |
(* (pow x 3) (- (+ (* 1/2 (/ eps (pow x 2))) (* 1/2 (/ 1 x))) (* 1/12 eps))) |
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)))) |
(* -1/12 (* eps (pow x 3))) |
(* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (* 1/2 (/ eps x)) (/ 1 (pow x 2)))) x)) (* -1/12 eps)))) |
(- 1 (* -1/2 (pow x 2))) |
(- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2))) |
(- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2))) |
(- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2))) |
(* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(* eps (- (/ 1 eps) (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(* eps (* x (+ 1/2 (* -1/12 (pow x 2))))) |
(* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (- (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* 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)))))))))) |
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))) |
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))) |
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))) |
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (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)))))))))) |
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))) |
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))) |
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))) |
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (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) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* 1/3840 (pow eps 5)) |
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 5)) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
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) (- (* 1/3840 (pow eps 2)) 1/48))) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* -1/48 eps) |
(* eps (- (* 1/3840 (pow eps 2)) 1/48)) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* eps (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)) |
(* -1/645120 (pow eps 5)) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120)) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* (pow eps 5) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4))))) |
(* -1/645120 (pow eps 5)) |
(* -1 (* (pow eps 5) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 5) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2)))))) |
(* 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)) |
(* -1/48 (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))))) |
(* -1/645120 (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)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 (pow eps 2)) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/120 eps) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* -1/2 x))) |
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))) |
(* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))) |
(* 1/12 (* eps (pow x 3))) |
(* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x)))) |
(* 1/12 (* eps (pow x 3))) |
(* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps)))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (* x (- (* 1/12 (pow x 2)) 1/2))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* eps (+ (* -1/2 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* -1 (* eps (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/12 (* eps x)) |
(* 1/4 (pow x 3)) |
(+ (* -1 (* eps (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)))) (* 1/4 (pow x 3))) |
(+ (* 1/4 (pow x 3)) (* eps (+ (* -1 (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2))) (* eps (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2)))))) |
(+ (* 1/4 (pow x 3)) (* eps (+ (* -1 (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2))) (* eps (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2)))))) |
(* (pow eps 2) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2))) |
(* (pow eps 2) (+ (* -1 (/ (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)) eps)) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2)))) |
(* (pow eps 2) (+ (* -1 (/ (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)) eps)) (+ (* 1/4 (/ (pow x 3) (pow eps 2))) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) |
(* (pow eps 2) (+ (* -1 (/ (* (pow x 2) (- (* 1/12 (pow x 2)) 1/2)) eps)) (+ (* 1/4 (/ (pow x 3) (pow eps 2))) (* x (pow (- (* 1/12 (pow x 2)) 1/2) 2))))) |
(* (pow eps 2) (* x (pow (+ 1/2 (* -1/12 (pow x 2))) 2))) |
(* (pow eps 2) (+ (* x (pow (+ 1/2 (* -1/12 (pow x 2))) 2)) (/ (* (pow x 2) (+ 1/2 (* -1/12 (pow x 2)))) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* (pow x 2) (+ 1/2 (* -1/12 (pow x 2))))) (* -1/4 (/ (pow x 3) eps))) eps)) (* x (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (* (pow x 2) (+ 1/2 (* -1/12 (pow x 2))))) (* -1/4 (/ (pow x 3) eps))) eps)) (* x (pow (+ 1/2 (* -1/12 (pow x 2))) 2)))) |
(* 1/4 (* (pow eps 2) x)) |
(* x (+ (* 1/4 (pow eps 2)) (* 1/2 (* eps x)))) |
(* x (+ (* 1/4 (pow eps 2)) (* x (+ (* 1/2 eps) (* x (+ 1/4 (* -1/12 (pow eps 2)))))))) |
(* x (+ (* 1/4 (pow eps 2)) (* x (+ (* 1/2 eps) (* x (+ 1/4 (+ (* -1/12 (* eps x)) (* -1/12 (pow eps 2))))))))) |
(* 1/144 (* (pow eps 2) (pow x 5))) |
(* (pow x 5) (+ (* -1/12 (/ eps x)) (* 1/144 (pow eps 2)))) |
(* (pow x 5) (+ (* -1/12 (/ eps x)) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/144 (pow eps 2)) (/ 1/4 (pow x 2)))))) |
(* (pow x 5) (+ (* -1/12 (/ eps x)) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/144 (pow eps 2)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1/4 (pow x 2))))))) |
(* 1/144 (* (pow eps 2) (pow x 5))) |
(* -1 (* (pow x 5) (+ (* -1/144 (pow eps 2)) (* 1/12 (/ eps x))))) |
(* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -1/12 eps) (+ (* -1/12 (/ (pow eps 2) x)) (* 1/4 (/ 1 x)))) x)) (* -1/144 (pow eps 2))))) |
(* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ 1/4 (* -1/12 (pow eps 2)))) (* -1/2 (/ eps x))) x)) (* -1/12 eps)) x)) (* -1/144 (pow eps 2))))) |
(* -1/48 (pow eps 2)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(* 1/3840 (pow eps 2)) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(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)))) |
| Outputs |
|---|
(* 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)) (* 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 #s(literal 2 binary64) eps) (*.f64 (cos.f64 x) #s(literal -1/12 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 #s(literal 2 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))))))))) |
(* -1/322560 (* (pow eps 7) (cos (+ x (* 1/2 eps))))) |
(*.f64 (*.f64 #s(literal -1/322560 binary64) (pow.f64 eps #s(literal 7 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (pow eps 7) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (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 (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (+.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)))) (*.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 (+ 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)))))) |
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.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 (*.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 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64))))))) |
(* -1/322560 (* (pow eps 7) (cos (- x (* -1/2 eps))))) |
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(* eps (* x (- (* 1/12 (pow x 2)) 1/2))) |
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(* eps (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
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(* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
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(* eps (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
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(* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
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(* -1 (* eps (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps)) (* -1 (pow x 2))) (* -1 (- 1 (* -1/2 (pow x 2))))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))))) |
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(/ (* eps (- 1 (* 1/4 (pow x 4)))) (- 1 (* -1/2 (pow x 2)))) |
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(* eps (- (+ (* eps (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
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(* eps (- (+ (* eps (- (+ (* eps (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
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(* eps (- (+ (* eps (- (+ (* eps (- (+ (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (/ (* eps (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/12 (pow x 2)) 1/2) 2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2)))))) (- (* 1/12 (pow x 2)) 1/2)))) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/12 (pow x 2)) 1/2) (- (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2)))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2)))))) (- 1 (* -1/2 (pow x 2))))))) (/ (* (pow x 3) (- (* 1/12 (pow x 2)) 1/2)) (- 1 (* -1/2 (pow x 2))))) (* -1 (/ (* x (* (- 1 (* 1/4 (pow x 4))) (- (* 1/12 (pow x 2)) 1/2))) (pow (- 1 (* -1/2 (pow x 2))) 2))))) (/ 1 (- 1 (* -1/2 (pow x 2))))) (* 1/4 (/ (pow x 4) (- 1 (* -1/2 (pow x 2))))))) |
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(* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))) |
(*.f64 (*.f64 eps eps) (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))) |
(* (pow eps 2) (- (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
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(* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (* x (- (* 1/12 (pow x 2)) 1/2)))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
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(* (pow eps 2) (- (+ (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (+ (* -1 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (- (* 1/12 (pow x 2)) 1/2)))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (- (* 1/12 (pow x 2)) 1/2)))))) (* (pow eps 3) (* x (- (* 1/12 (pow x 2)) 1/2))))))) (+ (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps))))) |
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(* -1 (* (pow eps 2) (* x (+ 1/2 (* -1/12 (pow x 2)))))) |
(*.f64 (*.f64 eps eps) (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64))))) |
(* (pow eps 2) (- (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (pow x 2) eps))) (* -1 (/ (- 1 (* -1/2 (pow x 2))) eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))) eps))) |
(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))))) eps)))) |
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(* (pow eps 2) (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* -1 (/ (+ (* -1 (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* -1 (/ (+ (* -1 (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (/ (- 1 (* 1/4 (pow x 4))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1 (/ (* (- 1 (* -1/2 (pow x 2))) (- (* -1 (pow x 2)) (* -1 (- 1 (* -1/2 (pow x 2)))))) (* x (+ 1/2 (* -1/12 (pow x 2)))))))) (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))) eps))) eps)))) |
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eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(+ eps (* x (- (* -1/2 (* eps x)) (* 1/2 (pow eps 2))))) |
(+.f64 eps (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))) |
(+ eps (* x (- (* x (- (* 1/12 (* (pow eps 2) x)) (* 1/2 eps))) (* 1/2 (pow eps 2))))) |
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(* 1/12 (* (pow eps 2) (pow x 3))) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (+ (* -1 (/ eps x)) (* 1/12 (pow eps 2))) (* -1/2 (/ eps x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) (/.f64 eps x)) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))) |
(* (pow x 3) (- (+ (* -1 (/ eps x)) (+ (* 1/12 (pow eps 2)) (* 12 (/ (+ 1/4 (* -1/12 (pow eps 2))) (pow x 2))))) (+ (* -6 (/ (- (* -1 eps) (* -1/2 eps)) (* eps (pow x 2)))) (+ (* -1/2 (/ eps x)) (* -1/2 (/ (pow eps 2) (pow x 2))))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 (* eps x))) |
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(+ 1 (* x (- (* 1/2 x) (* -1/2 eps)))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))))) |
(+ 1 (* x (- (* x (+ 1/2 (* -1/12 (* eps x)))) (* -1/2 eps)))) |
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(* -1/12 (* eps (pow x 3))) |
(*.f64 (*.f64 eps (*.f64 x (*.f64 x x))) #s(literal -1/12 binary64)) |
(* (pow x 3) (- (* 1/2 (/ 1 x)) (* 1/12 eps))) |
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(* -1/12 (* eps (pow x 3))) |
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(* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))) |
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(- 1 (* -1/2 (pow x 2))) |
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(- (+ 1 (* -1 (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) (* -1/2 (pow x 2))) |
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(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
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(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
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(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
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(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))) |
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(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(* 1/3840 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(+ (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 eps (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 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 (*.f64 x #s(literal -1/2 binary64)) (cos.f64 (*.f64 eps #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 (*.f64 #s(literal 1/6 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) |
Compiled 68036 to 4381 computations (93.6% saved)
24 alts after pruning (18 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1215 | 9 | 1224 |
| Fresh | 4 | 9 | 13 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1222 | 24 | 1246 |
| Status | Accuracy | Program |
|---|---|---|
| 37.1% | (-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x)) | |
| 62.9% | (-.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)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 62.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.7% | (+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) | |
| 98.4% | (+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) | |
| 52.1% | (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) | |
| 99.5% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) | |
| 53.4% | (*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) #s(literal 2 binary64)) | |
| ✓ | 99.5% | (*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
| 99.3% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) | |
| ✓ | 5.7% | (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
| 98.4% | (*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) | |
| 97.7% | (*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) | |
| 98.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) | |
| 98.4% | (*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) | |
| 97.6% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) | |
| ✓ | 98.4% | (*.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))))))))) |
| 98.3% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) | |
| 45.3% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps)))))) | |
| 98.9% | (*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) | |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| 5.8% | (*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) | |
| ✓ | 97.7% | eps |
Compiled 1410 to 542 computations (61.6% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.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 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.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)))))))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))))) |
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (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 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)))))))))) (cos.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 eps (*.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))))))) (*.f64 (*.f64 eps (*.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))))))))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps (*.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 (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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.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 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)))) |
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) (sin.f64 x)) |
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 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:
| 19.0ms | x |
| 15.0ms | eps |
| 12.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.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 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.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)))))))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))))) |
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (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 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)))))))))) (cos.f64 (/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (*.f64 eps eps) (*.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (*.f64 (*.f64 eps 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 eps 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 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps 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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 eps (*.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))))))) (*.f64 (*.f64 eps (*.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))))))))) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps (*.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 (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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
3 calls:
| 14.0ms | eps |
| 14.0ms | x |
| 11.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.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 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.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)))))))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
2 calls:
| 11.0ms | x |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.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 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 (sin.f64 (+.f64 x eps)) (*.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)))))))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
2 calls:
| 11.0ms | x |
| 8.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.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 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
2 calls:
| 10.0ms | x |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal 1/120 binary64) (pow.f64 eps #s(literal 5 binary64))) |
| Outputs |
|---|
(*.f64 eps (cos.f64 x)) |
2 calls:
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))))) 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 eps (*.f64 #s(literal 1/12 binary64) x)))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x)))))))))))) |
(sin.f64 eps) |
| Outputs |
|---|
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
2 calls:
| 8.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
2 calls:
| 20.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
2 calls:
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps 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 x (*.f64 eps #s(literal 1/12 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
2 calls:
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps eps)))))) |
| Outputs |
|---|
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
2 calls:
| 5.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.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 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 eps x))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
2 calls:
| 3.0ms | eps |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
Total -58.9b remaining (-3967.8%)
Threshold costs -58.9b (-3967.8%)
| Inputs |
|---|
eps |
(*.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 |
|---|
eps |
2 calls:
| 4.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 128× | *-commutative_binary64 |
| 76× | +-commutative_binary64 |
| 38× | sub-neg_binary64 |
| 34× | neg-sub0_binary64 |
| 34× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 92 | 214 |
| 1 | 172 | 214 |
| 2 | 191 | 214 |
| 3 | 211 | 214 |
| 4 | 244 | 214 |
| 5 | 270 | 214 |
| 6 | 295 | 214 |
| 7 | 311 | 214 |
| 8 | 316 | 214 |
| 9 | 319 | 214 |
| 10 | 320 | 214 |
| 1× | saturated |
| Inputs |
|---|
(*.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 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) 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 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 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 x (*.f64 eps #s(literal 1/12 binary64))))))))) |
(+.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
eps |
| 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)) |
(*.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 (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps (+.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)))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))))))) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 eps (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64)))))))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 binary64)))) (*.f64 x x)))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/12 binary64) x))) (*.f64 x x)) #s(literal 1 binary64)))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x #s(literal 1/12 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 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps x))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
eps |
| 6492× | *-lowering-*.f32 |
| 6492× | *-lowering-*.f64 |
| 5472× | *-lowering-*.f32 |
| 5472× | *-lowering-*.f64 |
| 5444× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1166 | 11310 |
| 1 | 4319 | 9918 |
| 0 | 9373 | 9918 |
| 0 | 6 | 16 |
| 1 | 51 | 16 |
| 2 | 413 | 16 |
| 3 | 5315 | 16 |
| 0 | 8737 | 16 |
| 0 | 528 | 5468 |
| 1 | 1880 | 4582 |
| 2 | 7053 | 4579 |
| 0 | 8074 | 4579 |
| 0 | 41 | 246 |
| 1 | 234 | 219 |
| 2 | 2006 | 219 |
| 0 | 8586 | 219 |
| 0 | 107 | 488 |
| 1 | 334 | 459 |
| 2 | 972 | 455 |
| 3 | 3571 | 455 |
| 0 | 8279 | 455 |
| 0 | 421 | 3850 |
| 1 | 1396 | 3373 |
| 2 | 4549 | 3332 |
| 0 | 8884 | 3332 |
| 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 778 to 474 computations (39.1% saved)
Compiled 480 to 210 computations (56.3% saved)
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