
Time bar (total: 17.7s)
| 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-tan: 8.0ms (25.3% of total)...c/correct-round.rkt:119:19: 7.0ms (22.1% of total)ival-mult: 3.0ms (9.5% of total)ival-fabs: 3.0ms (9.5% of total)ival-<=: 3.0ms (9.5% of total)ival-<: 3.0ms (9.5% of total)ival-add: 2.0ms (6.3% of total)ival-sub: 2.0ms (6.3% of total)ival-and: 1.0ms (3.2% of total)const: 0.0ms (0% of total)backward-pass: 0.0ms (0% of total)| 4.3s | 26063× | 0 | precondition |
| 1.2s | 4539× | 1 | valid |
| 520.0ms | 3717× | 0 | valid |
ival-mult: 833.0ms (18.3% of total)...c/correct-round.rkt:119:19: 793.0ms (17.4% of total)ival-tan: 661.0ms (14.5% of total)ival-sub: 585.0ms (12.8% of total)ival-<: 390.0ms (8.6% of total)ival-<=: 370.0ms (8.1% of total)ival-add: 329.0ms (7.2% of total)ival-fabs: 314.0ms (6.9% of total)ival-and: 135.0ms (3% of total)backward-pass: 99.0ms (2.2% of total)const: 49.0ms (1.1% of total)| 2× | egg-herbie |
| 376× | fnmadd-define |
| 344× | fnmsub-define |
| 344× | fmsub-define |
| 320× | sum3-define |
| 308× | fmm-def |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 46 |
| 1 | 43 | 42 |
| 2 | 94 | 42 |
| 3 | 198 | 42 |
| 4 | 507 | 42 |
| 5 | 917 | 42 |
| 6 | 1285 | 42 |
| 7 | 1548 | 42 |
| 8 | 1684 | 42 |
| 9 | 1711 | 42 |
| 0 | 6 | 7 |
| 1 | 9 | 7 |
| 2 | 14 | 7 |
| 3 | 21 | 7 |
| 4 | 31 | 7 |
| 5 | 63 | 7 |
| 6 | 122 | 7 |
| 7 | 210 | 7 |
| 8 | 295 | 7 |
| 9 | 401 | 7 |
| 10 | 479 | 7 |
| 11 | 485 | 7 |
| 0 | 485 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(- (tan (+ x eps)) (tan x)) |
| Outputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Inputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(- (tan (+ (neg x) eps)) (tan (neg x))) |
(- (tan (+ x (neg eps))) (tan x)) |
(neg (- (tan (+ (neg x) eps)) (tan (neg x)))) |
(neg (- (tan (+ x (neg eps))) (tan x))) |
(- (tan (+ eps x)) (tan eps)) |
| Outputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(- (tan (+ (neg x) eps)) (tan (neg x))) |
(+ (tan x) (tan (- eps x))) |
(- (tan (+ x (neg eps))) (tan x)) |
(- (tan (- x eps)) (tan x)) |
(neg (- (tan (+ (neg x) eps)) (tan (neg x)))) |
(- (tan (- x eps)) (tan x)) |
(neg (- (tan (+ x (neg eps))) (tan x))) |
(+ (tan x) (tan (- eps x))) |
(- (tan (+ eps x)) (tan eps)) |
(- (tan (+ x eps)) (tan eps)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 228 | 3 | (-4.28718533615325e-244 2.596565261760719e-246) | 4 | (-3.078977089395929e-248 4.894015027365364e-250) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4 | 0 | - | 0 | - | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | eps |
| 47.0ms | 276× | 1 | valid |
| 20.0ms | 234× | 0 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 51 to 20 computations (60.8% saved)
ival-tan: 15.0ms (43.5% of total)backward-pass: 10.0ms (29% of total)ival-add: 5.0ms (14.5% of total)ival-sub: 4.0ms (11.6% of total)const: 1.0ms (2.9% of total)Compiled 9 to 6 computations (33.3% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.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 | (tan.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (tan.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 124× | fnmadd-define |
| 122× | sum3-define |
| 80× | fma-lowering-fma.f32 |
| 80× | fnmsub-define |
| 80× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 9 | 18 |
| 2 | 14 | 18 |
| 3 | 21 | 18 |
| 4 | 31 | 18 |
| 5 | 63 | 18 |
| 6 | 122 | 18 |
| 7 | 210 | 18 |
| 8 | 295 | 18 |
| 9 | 401 | 18 |
| 10 | 479 | 18 |
| 11 | 485 | 18 |
| 0 | 485 | 18 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(tan (+ x eps)) |
(+ x eps) |
x |
eps |
(tan x) |
| Outputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan (+ x eps)) |
(tan.f64 (+.f64 x eps)) |
(+ x eps) |
(+.f64 x eps) |
x |
eps |
(tan x) |
(tan.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x eps) |
| ✓ | accuracy | 100.0% | (tan.f64 x) |
| ✓ | accuracy | 99.7% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 62.2% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 22.0ms | 138× | 1 | valid |
| 11.0ms | 117× | 0 | valid |
| 1.0ms | 1× | 3 | valid |
Compiled 21 to 7 computations (66.7% saved)
ival-tan: 7.0ms (49.7% of total)ival-add: 3.0ms (21.3% of total)backward-pass: 2.0ms (14.2% of total)ival-sub: 2.0ms (14.2% of total)const: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- (tan (+ x eps)) (tan x))> |
#<alt (tan (+ x eps))> |
#<alt (+ x eps)> |
#<alt (tan x)> |
| Outputs |
|---|
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- 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 (* 1/3 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 2.0ms | eps | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 2.0ms | eps | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | -inf | (- (tan (+ x eps)) (tan x)) |
| 1× | batch-egg-rewrite |
| 3856× | *-lowering-*.f32 |
| 3856× | *-lowering-*.f64 |
| 3276× | /-lowering-/.f32 |
| 3276× | /-lowering-/.f64 |
| 1940× | fma-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 46 | 16 |
| 2 | 419 | 16 |
| 3 | 6555 | 16 |
| 0 | 8507 | 16 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (tan (+ x eps)) (tan x)) |
(tan (+ x eps)) |
(+ x eps) |
(tan x) |
| Outputs |
|---|
(+.f64 (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x) (tan.f64 x))) |
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))))) |
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(-.f64 (/.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))) |
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x)) |
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
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(/.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 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 (*.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 #s(literal 1 binary64) (+.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 (/.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)))) |
(tan.f64 x) |
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
(*.f64 #s(literal 1 binary64) (tan.f64 x)) |
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) |
| 1× | egg-herbie |
| 3412× | *-lowering-*.f32 |
| 3412× | *-lowering-*.f64 |
| 2990× | fma-lowering-fma.f32 |
| 2990× | fma-lowering-fma.f64 |
| 2652× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 157 | 1381 |
| 1 | 494 | 1286 |
| 2 | 1891 | 1261 |
| 3 | 7721 | 1261 |
| 0 | 8567 | 1261 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- 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 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 x (-.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x (-.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1/6 binary64) (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))))))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.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 (* 1/3 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
Compiled 8812 to 983 computations (88.8% saved)
17 alts after pruning (16 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 307 | 16 | 323 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 307 | 17 | 324 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.3% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| 62.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) | |
| ▶ | 61.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| 60.9% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) | |
| ▶ | 97.2% | (/.f64 (sin.f64 eps) (cos.f64 eps)) |
| 62.2% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 61.9% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 61.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) | |
| 60.7% | (-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) | |
| 60.5% | (-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) | |
| ✓ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 60.4% | (-.f64 (tan.f64 (+.f64 x eps)) x) |
| 100.0% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| 99.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| ▶ | 100.0% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
Compiled 1051 to 456 computations (56.6% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (tan.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 (tan.f64 x) (tan.f64 eps)) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 6400 | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (cos.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
| ✓ | cost-diff | 6528 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | cost-diff | 0 | (cos.f64 eps) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 0 | (/.f64 (sin.f64 eps) (cos.f64 eps)) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (tan.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) x) |
| ✓ | cost-diff | 143744 | (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) |
| ✓ | cost-diff | 156416 | (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 163008 | (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
| ✓ | cost-diff | 163008 | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| 3172× | --lowering--.f32 |
| 3172× | --lowering--.f64 |
| 2988× | *-lowering-*.f32 |
| 2988× | *-lowering-*.f64 |
| 2300× | +-lowering-+.f64 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 1754 |
| 1 | 182 | 1468 |
| 2 | 696 | 1162 |
| 3 | 3325 | 1049 |
| 0 | 8458 | 1049 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
eps |
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
1 |
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) |
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))) |
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (sin x) (cos x)) |
(sin x) |
x |
(cos x) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(pow (sin x) 2) |
2 |
(pow (cos x) 2) |
(* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))) |
(- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))) |
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
-1/6 |
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
-1/2 |
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) |
(* -1/2 (pow (sin x) 2)) |
(- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) |
(* 1/6 (pow (sin x) 2)) |
1/6 |
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))) |
(+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)) |
(/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) |
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3) |
-1/3 |
(- (tan (+ x eps)) x) |
(tan (+ x eps)) |
(+ x eps) |
x |
eps |
(/ (sin eps) (cos eps)) |
(sin eps) |
eps |
(cos eps) |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x))) |
(/ 1 (cos (+ x eps))) |
1 |
(cos (+ x eps)) |
(+ x eps) |
x |
eps |
(sin (+ x eps)) |
(- 0 (tan x)) |
0 |
(tan x) |
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x))) |
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) |
(+ (tan x) (tan eps)) |
(tan x) |
x |
(tan eps) |
eps |
(- 1 (pow (* (tan x) (tan eps)) 2)) |
1 |
(pow (* (tan x) (tan eps)) 2) |
(* (tan x) (tan eps)) |
2 |
(+ 1 (* (tan x) (tan eps))) |
(- 0 (tan x)) |
0 |
| Outputs |
|---|
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
eps |
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
1 |
#s(literal 1 binary64) |
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+.f64 (*.f64 eps (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) |
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) |
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))))) |
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))) |
(+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))) |
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(sin x) |
(sin.f64 x) |
x |
(cos x) |
(cos.f64 x) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
2 |
#s(literal 2 binary64) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))) |
(*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))) |
(- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))) |
(-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))) |
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) |
-1/6 |
#s(literal -1/6 binary64) |
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))) |
-1/2 |
#s(literal -1/2 binary64) |
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) |
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/2 (pow (sin x) 2)) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -5/6 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) |
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* 1/6 (pow (sin x) 2)) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) |
1/6 |
#s(literal 1/6 binary64) |
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) |
(* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))) |
(*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) |
(+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)) |
(+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) |
(/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) |
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))) |
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))) |
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(-.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) |
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3) |
(*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- (tan (+ x eps)) x) |
(-.f64 (tan.f64 (+.f64 eps x)) x) |
(tan (+ x eps)) |
(tan.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin eps) |
(sin.f64 eps) |
eps |
(cos eps) |
(cos.f64 eps) |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/ 1 (cos (+ x eps))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
1 |
#s(literal 1 binary64) |
(cos (+ x eps)) |
(cos.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(- 0 (tan x)) |
(-.f64 #s(literal 0 binary64) (tan.f64 x)) |
0 |
#s(literal 0 binary64) |
(tan x) |
(tan.f64 x) |
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x))) |
(-.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (tan.f64 x)) |
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) |
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) |
(+ (tan x) (tan eps)) |
(+.f64 (tan.f64 x) (tan.f64 eps)) |
(tan x) |
(tan.f64 x) |
x |
(tan eps) |
(tan.f64 eps) |
eps |
(- 1 (pow (* (tan x) (tan eps)) 2)) |
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) |
1 |
#s(literal 1 binary64) |
(pow (* (tan x) (tan eps)) 2) |
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) |
(* (tan x) (tan eps)) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
2 |
#s(literal 2 binary64) |
(+ 1 (* (tan x) (tan eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(- 0 (tan x)) |
(-.f64 #s(literal 0 binary64) (tan.f64 x)) |
0 |
#s(literal 0 binary64) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 (tan.f64 x) (tan.f64 eps)) |
| ✓ | accuracy | 100.0% | (+.f64 (tan.f64 x) (tan.f64 eps)) |
| ✓ | accuracy | 99.9% | (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) |
| ✓ | accuracy | 92.4% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | accuracy | 100.0% | (tan.f64 x) |
| ✓ | accuracy | 99.9% | (cos.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 92.4% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | accuracy | 100.0% | (sin.f64 eps) |
| ✓ | accuracy | 100.0% | (cos.f64 eps) |
| ✓ | accuracy | 100.0% | (/.f64 (sin.f64 eps) (cos.f64 eps)) |
| ✓ | accuracy | 100.0% | (+.f64 x eps) |
| ✓ | accuracy | 99.8% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 92.8% | (-.f64 (tan.f64 (+.f64 x eps)) x) |
| ✓ | accuracy | 99.7% | (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) |
| ✓ | accuracy | 99.3% | (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) |
| ✓ | accuracy | 99.3% | (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) |
| 440.0ms | 138× | 5 | exit |
| 93.0ms | 107× | 0 | valid |
| 19.0ms | 3× | 3 | valid |
| 11.0ms | 8× | 1 | valid |
Compiled 1811 to 60 computations (96.7% saved)
backward-pass: 90.0ms (26.7% of total)ival-mult: 60.0ms (17.8% of total)compiled-spec: 39.0ms (11.6% of total)ival-sin: 28.0ms (8.3% of total)ival-add: 24.0ms (7.1% of total)ival-div: 21.0ms (6.2% of total)ival-tan: 18.0ms (5.3% of total)...c/correct-round.rkt:119:19: 17.0ms (5% of total)ival-pow: 16.0ms (4.7% of total)ival-sub: 12.0ms (3.6% of total)ival-cos: 9.0ms (2.7% of total)const: 1.0ms (0.3% of total)| Inputs |
|---|
#<alt (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))> |
#<alt (- (tan (+ x eps)) x)> |
#<alt (tan (+ x eps))> |
#<alt (+ x eps)> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (sin eps)> |
#<alt (cos eps)> |
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))> |
#<alt (/ 1 (cos (+ x eps)))> |
#<alt (cos (+ x eps))> |
#<alt (+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x)))> |
#<alt (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))> |
#<alt (+ (tan x) (tan eps))> |
#<alt (tan x)> |
#<alt (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))> |
#<alt (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))> |
#<alt (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)> |
#<alt (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))))> |
#<alt (sin (+ x eps))> |
#<alt (pow (* (tan x) (tan eps)) 2)> |
#<alt (* (tan x) (tan eps))> |
| Outputs |
|---|
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))> |
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (* -1 x)> |
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))> |
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))> |
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))> |
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))> |
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))> |
#<alt (- (/ (sin x) (cos x)) x)> |
#<alt (- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)> |
#<alt (- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)> |
#<alt (- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- 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 eps> |
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt eps> |
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#<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 1> |
#<alt (+ 1 (* -1/2 (pow eps 2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (/ 1 (cos eps))> |
#<alt (+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))> |
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))> |
#<alt (/ 1 (cos (+ eps x)))> |
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#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))> |
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#<alt (+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
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#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
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#<alt (* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
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#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
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#<alt (- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
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#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
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#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
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#<alt (/ (sin x) (cos x))> |
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#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
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#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
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#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))> |
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#<alt x> |
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#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt -1/3> |
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#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))> |
#<alt 1/3> |
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#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1/3 x)> |
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#<alt (* x (- (* (pow x 2) (- (* -601/360 (pow x 2)) 23/18)) 1/3))> |
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -23183/15120 (pow x 2)) 601/360)) 23/18)) 1/3))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))> |
#<alt (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos 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 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))> |
#<alt (* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))> |
#<alt (* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))> |
#<alt (* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))> |
#<alt (* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))> |
#<alt (/ (* x (sin eps)) (cos eps))> |
#<alt (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))> |
#<alt (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))> |
#<alt (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* eps (sin x)) (cos x))> |
#<alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))> |
#<alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))> |
#<alt (* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
120 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 30.0ms | x | @ | -inf | (+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x))) |
| 13.0ms | x | @ | -inf | (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
| 8.0ms | x | @ | inf | (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
| 7.0ms | eps | @ | 0 | (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
| 3.0ms | x | @ | inf | (+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x))) |
| 1× | batch-egg-rewrite |
| 3442× | *-lowering-*.f32 |
| 3442× | *-lowering-*.f64 |
| 2488× | /-lowering-/.f32 |
| 2488× | /-lowering-/.f64 |
| 1938× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 850 |
| 1 | 477 | 452 |
| 2 | 5906 | 442 |
| 0 | 8182 | 442 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (/ (* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) |
(- (tan (+ x eps)) x) |
(tan (+ x eps)) |
(+ x eps) |
(/ (sin eps) (cos eps)) |
(sin eps) |
(cos eps) |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x))) |
(/ 1 (cos (+ x eps))) |
(cos (+ x eps)) |
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (- 0 (tan x))) |
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) |
(+ (tan x) (tan eps)) |
(tan x) |
(+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(- -1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3) |
(* (sin x) (+ 1/6 (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (- (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(sin (+ x eps)) |
(pow (* (tan x) (tan eps)) 2) |
(* (tan x) (tan eps)) |
| Outputs |
|---|
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
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(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) |
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(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))) (exp.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (tan.f64 eps)) |
(*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 eps)) (tan.f64 x)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(/.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (cos.f64 x))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) |
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))) |
(/.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 eps))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))) |
(/.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (cos.f64 eps) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (sin.f64 x)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 x))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) |
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)) |
(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)) |
(/.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) |
(/.f64 (*.f64 (tan.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x))) |
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))) |
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) |
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps))) |
(*.f64 (sin.f64 eps) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x))) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (tan.f64 eps) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(*.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x))) |
| 1× | egg-herbie |
| 5526× | +-lowering-+.f64 |
| 5526× | +-lowering-+.f32 |
| 4372× | *-lowering-*.f32 |
| 4372× | *-lowering-*.f64 |
| 1872× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 795 | 15992 |
| 1 | 2801 | 15392 |
| 0 | 8314 | 15392 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps)))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps)))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(* -1 x) |
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1)) |
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1)) |
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1)) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x))))))))) |
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x))))))))) |
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x))))))))) |
(- (/ (sin x) (cos x)) x) |
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x) |
(- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x) |
(- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) x) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin x) (cos x)) |
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(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- 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))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos eps)) |
(/ (sin eps) (cos 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) |
1 |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ 1 (cos eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
-1/3 |
(- (* -4/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1/3 x) |
(* x (- (* -4/9 (pow x 2)) 1/3)) |
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3)) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* -1/3 x) |
(* x (- (* -23/18 (pow x 2)) 1/3)) |
(* x (- (* (pow x 2) (- (* -601/360 (pow x 2)) 23/18)) 1/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -23183/15120 (pow x 2)) 601/360)) 23/18)) 1/3)) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) |
(* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos 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))) |
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) |
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* x (sin eps)) (cos eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
| Outputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))))) (/.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) |
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1/3 |
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(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 62/315 binary64) (*.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) |
(/ (* x (sin eps)) (cos eps)) |
(/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps))))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 2/15 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)))))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 17/315 binary64) (/.f64 (*.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps)))))))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* eps (sin x)) (cos x)) |
(/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)))))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x)))))))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
Compiled 65270 to 3890 computations (94% saved)
25 alts after pruning (23 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1190 | 17 | 1207 |
| Fresh | 5 | 6 | 11 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1199 | 25 | 1224 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 62.3% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| 62.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) | |
| ▶ | 60.5% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
| 61.5% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) | |
| 60.9% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) | |
| 97.2% | (/.f64 eps (cos.f64 eps)) | |
| 62.2% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 61.9% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 61.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| ✓ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 100.0% | (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) | |
| ▶ | 100.0% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
| 97.3% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) | |
| ▶ | 97.4% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
| 99.7% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) | |
| 97.3% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) | |
| 97.4% | (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| 99.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x))))) | |
| 98.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| ▶ | 98.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| 97.4% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) | |
| 97.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) | |
| ▶ | 97.2% | eps |
Compiled 1378 to 739 computations (46.4% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 256 | (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) |
| ✓ | cost-diff | 256 | (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 256 | (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
| ✓ | cost-diff | 256 | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| ✓ | cost-diff | 0 | (cos.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))) |
| ✓ | cost-diff | 6528 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
| ✓ | cost-diff | 384 | (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) |
| ✓ | cost-diff | 384 | (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
| ✓ | cost-diff | 512 | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
| ✓ | cost-diff | 32640 | (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))) |
| ✓ | cost-diff | 38976 | (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) |
| ✓ | cost-diff | 38976 | (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) |
| ✓ | cost-diff | 38976 | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
| 3232× | *-lowering-*.f32 |
| 3232× | *-lowering-*.f64 |
| 2524× | +-lowering-+.f64 |
| 2524× | +-lowering-+.f32 |
| 1662× | fma-lowering-fma.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 1168 |
| 1 | 269 | 1059 |
| 2 | 1122 | 1008 |
| 3 | 4923 | 998 |
| 0 | 8132 | 998 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
eps |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(pow (tan x) 2) |
(tan x) |
x |
2 |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))) |
(+ (tan x) (pow (tan x) 3)) |
(pow (tan x) 3) |
3 |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) |
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(- 1/3 (* (pow (tan x) 2) -1/3)) |
1/3 |
(* (pow (tan x) 2) -1/3) |
-1/3 |
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) |
(+ 1 (pow (tan x) 2)) |
1 |
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))) |
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)) |
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) |
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) |
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
eps |
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))) |
(* eps (+ 1 (* 1/3 (* eps eps)))) |
eps |
(+ 1 (* 1/3 (* eps eps))) |
1 |
(* 1/3 (* eps eps)) |
1/3 |
(* eps eps) |
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))) |
x |
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))) |
(* eps (* x (+ 1 (* (* eps eps) 4/3)))) |
(* x (+ 1 (* (* eps eps) 4/3))) |
(+ 1 (* (* eps eps) 4/3)) |
(* (* eps eps) 4/3) |
4/3 |
(* (* eps eps) (+ 1 (* (* eps eps) 2/3))) |
(+ 1 (* (* eps eps) 2/3)) |
(* (* eps eps) 2/3) |
2/3 |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x)))))) |
(/ 1 (cos (+ x eps))) |
1 |
(cos (+ x eps)) |
(+ x eps) |
x |
eps |
(sin (+ x eps)) |
(- 0 (* x (+ 1 (* 1/3 (* x x))))) |
0 |
(* x (+ 1 (* 1/3 (* x x)))) |
(+ 1 (* 1/3 (* x x))) |
(* 1/3 (* x x)) |
1/3 |
(* x x) |
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
eps |
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
1 |
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) |
(* 1/3 (* eps eps)) |
1/3 |
(* eps eps) |
(* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))) |
x |
(+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))) |
(* eps (+ 1 (* (* eps eps) 2/3))) |
(+ 1 (* (* eps eps) 2/3)) |
(* (* eps eps) 2/3) |
2/3 |
(* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))) |
(+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))) |
(* (* eps eps) 4/3) |
4/3 |
(* eps (* x (+ 4/3 (* (* eps eps) 17/9)))) |
(* x (+ 4/3 (* (* eps eps) 17/9))) |
(+ 4/3 (* (* eps eps) 17/9)) |
(* (* eps eps) 17/9) |
17/9 |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(pow (sin x) 2) |
(sin x) |
2 |
(pow (cos x) 2) |
(cos x) |
| Outputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))))))) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
(*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))))))) |
eps |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))))) |
(pow (tan x) 2) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan x) |
(tan.f64 x) |
x |
2 |
#s(literal 2 binary64) |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))))))) |
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))) |
(+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))))) |
(+ (tan x) (pow (tan x) 3)) |
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) |
(pow (tan x) 3) |
(pow.f64 (tan.f64 x) #s(literal 3 binary64)) |
3 |
#s(literal 3 binary64) |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))) |
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) |
(+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))) |
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(- 1/3 (* (pow (tan x) 2) -1/3)) |
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* (pow (tan x) 2) -1/3) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(+ 1 (pow (tan x) 2)) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))) |
(*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) |
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)) |
(*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) |
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) |
(*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) |
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) |
(+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
eps |
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64))))))))) |
(* eps (+ 1 (* 1/3 (* eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))) |
eps |
(+ 1 (* 1/3 (* eps eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))) |
1 |
#s(literal 1 binary64) |
(* 1/3 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))) |
(*.f64 eps (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64)))))))) |
x |
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))) |
(*.f64 eps (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 eps #s(literal 2/3 binary64)) (*.f64 x #s(literal 4/3 binary64))))))) |
(* eps (* x (+ 1 (* (* eps eps) 4/3)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 eps x)) |
(* x (+ 1 (* (* eps eps) 4/3))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
(+ 1 (* (* eps eps) 4/3)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(* (* eps eps) 4/3) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
4/3 |
#s(literal 4/3 binary64) |
(* (* eps eps) (+ 1 (* (* eps eps) 2/3))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) |
(+ 1 (* (* eps eps) 2/3)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) |
(* (* eps eps) 2/3) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
2/3 |
#s(literal 2/3 binary64) |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x)))))) |
(+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (*.f64 x (-.f64 (*.f64 x (*.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64)))) |
(/ 1 (cos (+ x eps))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
1 |
#s(literal 1 binary64) |
(cos (+ x eps)) |
(cos.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(- 0 (* x (+ 1 (* 1/3 (* x x))))) |
(*.f64 x (-.f64 (*.f64 x (*.f64 x #s(literal -1/3 binary64))) #s(literal 1 binary64))) |
0 |
#s(literal 0 binary64) |
(* x (+ 1 (* 1/3 (* x x)))) |
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/3 binary64))))) |
(+ 1 (* 1/3 (* x x))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))) |
(* 1/3 (* x x)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* x x) |
(*.f64 x x) |
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
eps |
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
1 |
#s(literal 1 binary64) |
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))) (*.f64 x x)) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(* 1/3 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))) |
(*.f64 x (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 x (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64)))))))) |
x |
(+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 x (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64))))))) |
(* eps (+ 1 (* (* eps eps) 2/3))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) |
(+ 1 (* (* eps eps) 2/3)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) |
(* (* eps eps) 2/3) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
2/3 |
#s(literal 2/3 binary64) |
(* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))) |
(*.f64 (*.f64 eps x) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64))))) |
(+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))) |
(*.f64 eps (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps (+.f64 (*.f64 x (*.f64 eps #s(literal 17/9 binary64))) #s(literal 4/3 binary64))))) |
(* (* eps eps) 4/3) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
4/3 |
#s(literal 4/3 binary64) |
(* eps (* x (+ 4/3 (* (* eps eps) 17/9)))) |
(*.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 eps x)) |
(* x (+ 4/3 (* (* eps eps) 17/9))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(+ 4/3 (* (* eps eps) 17/9)) |
(+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) |
(* (* eps eps) 17/9) |
(*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) |
17/9 |
#s(literal 17/9 binary64) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin x) |
(sin.f64 x) |
2 |
#s(literal 2 binary64) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos x) |
(cos.f64 x) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.9% | (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 93.0% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
| ✓ | accuracy | 99.9% | (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.9% | (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))) |
| ✓ | accuracy | 99.8% | (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) |
| ✓ | accuracy | 99.7% | (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
| 481.0ms | 137× | 5 | exit |
| 91.0ms | 112× | 0 | valid |
| 11.0ms | 3× | 2 | valid |
| 7.0ms | 4× | 1 | valid |
Compiled 1312 to 76 computations (94.2% saved)
backward-pass: 108.0ms (33% of total)ival-mult: 72.0ms (22% of total)ival-pow: 40.0ms (12.2% of total)ival-add: 39.0ms (11.9% of total)...c/correct-round.rkt:119:19: 29.0ms (8.9% of total)ival-sub: 8.0ms (2.4% of total)compiled-spec: 7.0ms (2.1% of total)ival-cos: 7.0ms (2.1% of total)ival-div: 6.0ms (1.8% of total)ival-sin: 6.0ms (1.8% of total)ival-tan: 4.0ms (1.2% of total)const: 1.0ms (0.3% of total)| Inputs |
|---|
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)> |
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))> |
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))> |
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))> |
#<alt (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))> |
#<alt (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))> |
#<alt (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))> |
#<alt (* eps (+ 1 (* 1/3 (* eps eps))))> |
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x))))))> |
#<alt (- 0 (* x (+ 1 (* 1/3 (* x x)))))> |
#<alt (/ 1 (cos (+ x eps)))> |
#<alt (cos (+ x eps))> |
#<alt (* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9)))))))))> |
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)> |
#<alt (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))> |
#<alt (* (pow (tan x) 2) -1/3)> |
#<alt (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))> |
#<alt (* 1/3 (* eps eps))> |
#<alt (* (* eps eps) 2/3)> |
#<alt (* (* eps eps) 4/3)> |
#<alt (sin (+ x eps))> |
#<alt (* 1/3 (* x x))> |
#<alt (* x (+ 4/3 (* (* eps eps) 17/9)))> |
| Outputs |
|---|
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))> |
#<alt (* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))> |
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#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (+ (* eps x) (pow x 2))))> |
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#<alt (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))> |
#<alt (* 2/3 (* (pow eps 4) x))> |
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#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))> |
#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))> |
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#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))> |
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#<alt (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))> |
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#<alt (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))> |
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#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
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#<alt (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))> |
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#<alt (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (+ (* eps x) (pow x 2)))> |
#<alt (* eps (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2)))> |
#<alt (* eps (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2)))> |
#<alt (* 2/3 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))> |
#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2)))))> |
#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))> |
#<alt (* 2/3 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))> |
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#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))> |
#<alt (* eps x)> |
#<alt (* eps (+ eps x))> |
#<alt (* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))> |
#<alt (* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))))> |
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#<alt (* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))> |
#<alt (* 2/3 (pow eps 4))> |
#<alt (* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))> |
#<alt (* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps))))> |
#<alt (* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))> |
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#<alt (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))> |
#<alt (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))> |
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#<alt (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))> |
#<alt (* eps (* x (+ 1 (* 4/3 (pow eps 2)))))> |
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#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))> |
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))> |
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))> |
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))> |
#<alt (* 1/3 (pow eps 3))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (* 1/3 (pow eps 3))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (* -1/3 (pow x 3))> |
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#<alt (* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2)))))> |
#<alt (* -1/3 (pow x 3))> |
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#<alt (* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2))))))> |
#<alt (- (/ (sin x) (cos x)) (* x (+ 1 (* 1/3 (pow x 2)))))> |
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#<alt (- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2)))))> |
#<alt (* -1 x)> |
#<alt (* x (- (* -1/3 (pow x 2)) 1))> |
#<alt (* x (- (* -1/3 (pow x 2)) 1))> |
#<alt (* x (- (* -1/3 (pow x 2)) 1))> |
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#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))> |
#<alt (* -1/3 (pow x 2))> |
#<alt (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))> |
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* 1/3 eps)> |
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))> |
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))> |
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 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 (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* 1/3 (pow x 2))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* x (+ 4/3 (* 17/9 (pow eps 2))))> |
#<alt (* 4/3 x)> |
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))> |
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))> |
#<alt (+ (* 4/3 x) (* 17/9 (* (pow eps 2) x)))> |
#<alt (* 17/9 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
#<alt (* 17/9 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
#<alt (* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x)))> |
129 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | eps | @ | 0 | (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) |
| 9.0ms | x | @ | inf | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 5.0ms | x | @ | -inf | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 4.0ms | eps | @ | inf | (sin (+ x eps)) |
| 3.0ms | eps | @ | 0 | (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))) |
| 1× | batch-egg-rewrite |
| 3804× | *-lowering-*.f32 |
| 3804× | *-lowering-*.f64 |
| 2166× | +-lowering-+.f64 |
| 2166× | +-lowering-+.f32 |
| 1968× | /-lowering-/.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 656 |
| 1 | 613 | 569 |
| 2 | 7098 | 566 |
| 0 | 8233 | 566 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))) |
(* x (+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))) |
(+ (* eps (* x (+ 1 (* (* eps eps) 4/3)))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))) |
(* eps (+ 1 (* 1/3 (* eps eps)))) |
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (* x (+ 1 (* 1/3 (* x x)))))) |
(- 0 (* x (+ 1 (* 1/3 (* x x))))) |
(/ 1 (cos (+ x eps))) |
(cos (+ x eps)) |
(* eps (+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* 1/3 (* eps eps)) (* x (+ (* eps (+ 1 (* (* eps eps) 2/3))) (* x (+ (* (* eps eps) 4/3) (* eps (* x (+ 4/3 (* (* eps eps) 17/9))))))))) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) |
(* (pow (tan x) 2) -1/3) |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(* 1/3 (* eps eps)) |
(* (* eps eps) 2/3) |
(* (* eps eps) 4/3) |
(sin (+ x eps)) |
(* 1/3 (* x x)) |
(* x (+ 4/3 (* (* eps eps) 17/9))) |
| Outputs |
|---|
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps) |
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)) |
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps))) |
(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps eps) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))))) (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) eps) (-.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 2 binary64)) (*.f64 eps eps)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))))))) |
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(sin.f64 (+.f64 eps x)) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))) |
(*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) |
(*.f64 (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64))) x) |
(+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(+.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 x #s(literal 4/3 binary64))) |
(fma.f64 x #s(literal 4/3 binary64) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(fma.f64 #s(literal 4/3 binary64) x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x #s(literal 4/3 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) (*.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x #s(literal 4/3 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))) (-.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))) |
(/.f64 (*.f64 x (+.f64 #s(literal 64/27 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64))))) (+.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) #s(literal 4/3 binary64))))) |
(/.f64 (*.f64 x (-.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64)))) (-.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(/.f64 (*.f64 (+.f64 #s(literal 64/27 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64)))) x) (+.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)) #s(literal 4/3 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 16/9 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 289/81 binary64))) x) (-.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(*.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))) x) |
| 1× | egg-herbie |
| 5576× | *-lowering-*.f32 |
| 5576× | *-lowering-*.f64 |
| 5254× | +-lowering-+.f64 |
| 5254× | +-lowering-+.f32 |
| 1730× | distribute-lft-in |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 939 | 17262 |
| 1 | 3430 | 16961 |
| 0 | 8748 | 16961 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) |
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
(* 1/3 (pow eps 3)) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps x) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x))) |
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x))) |
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))) |
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))) |
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))) |
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* eps (pow x 2)) |
(* eps (+ (* eps x) (pow x 2))) |
(* eps (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2))) |
(* eps (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps)))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x))) |
(* eps x) |
(* eps (+ eps x)) |
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x)))))) |
(* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x))))))) |
(* 2/3 (pow eps 4)) |
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps)))) |
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))))) |
(* 2/3 (pow eps 4)) |
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps)))) |
(* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps)))) |
(* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps)))) |
(* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) |
(* eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
eps |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(* -1/3 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2))))) |
(* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1/3 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (+ 1/3 (+ (* -1 (/ (sin (- eps (* -1 x))) (* (pow x 3) (cos (- eps (* -1 x)))))) (/ 1 (pow x 2)))))) |
(- (/ (sin x) (cos x)) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* 1/3 (pow x 2))))) |
(* -1 x) |
(* x (- (* -1/3 (pow x 2)) 1)) |
(* x (- (* -1/3 (pow x 2)) 1)) |
(* x (- (* -1/3 (pow x 2)) 1)) |
(* -1/3 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1/3 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))) |
(/ 1 (cos eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 4) (* x (+ 2/3 (* 17/9 (pow x 2))))) |
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)))))) |
(* (pow eps 4) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))) |
(* -1 (* (pow eps 4) (* x (- (* -17/9 (pow x 2)) 2/3)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* -17/9 (pow x 2)) 2/3))) (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ (* -1 (* x (- (* -4/3 (pow x 2)) 1))) (+ (/ 1 eps) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps)))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* (pow eps 2) (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (+ (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 3) x)) (+ (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ (* eps (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow x 3)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))) |
(* (pow eps 2) (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 3) x)) (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2)))))))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 3)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 2) (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))) x))) x)) (* 4/3 (pow eps 3))) x))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))))) |
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* x (- (* -4/3 (pow x 2)) 1))) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2)))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ 1 (pow x 3)) (+ (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)) (/ (pow (sin x) 2) (* (pow x 3) (pow (cos x) 2))))))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2)))))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ 1 (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))) x)) (* 4/3 (pow eps 2))) x))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* x (- (* -4/3 (pow x 2)) 1))) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2)))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)) (/ (pow (sin x) 2) (* (pow x 3) (pow (cos x) 2)))))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2)))))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ (* 1/3 (pow eps 2)) (/ (pow (sin x) 2) (pow (cos x) 2))) x))) x)) (* 4/3 (pow eps 2))) x))))) |
(* eps (* x (+ 1 (* 4/3 (pow x 2))))) |
(* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (* eps (* x (+ 2/3 (* 17/9 (pow x 2)))))))) (* x (+ 1 (* 4/3 (pow x 2)))))) |
(* (pow eps 3) (* x (+ 2/3 (* 17/9 (pow x 2))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)))))) |
(* (pow eps 3) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* x (+ 2/3 (* 17/9 (pow x 2)))) (+ (* 1/3 (/ 1 eps)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) (pow eps 2)))))) |
(* -1 (* (pow eps 3) (* x (- (* -17/9 (pow x 2)) 2/3)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (* x (- (* -4/3 (pow x 2)) 1)) eps)) (* 4/3 (pow x 2)))) eps)) (* x (- (* -17/9 (pow x 2)) 2/3))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (* eps (+ 4/3 (* 17/9 (pow eps 2)))))) |
(* (pow x 3) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 2) (pow x 3))) (+ (* 4/3 (/ (pow eps 2) x)) (+ (* eps (+ 4/3 (* 17/9 (pow eps 2)))) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) (pow x 2)))))) |
(* eps (* (pow x 3) (+ 4/3 (* 17/9 (pow eps 2))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (/ (pow eps 2) x)) (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2)))))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 4/3 (* 17/9 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))) x))))) |
(* -1/3 x) |
(* x (- (* -4/9 (pow x 2)) 1/3)) |
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3)) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 x) |
(* x (- (* -13/9 (pow x 2)) 1/3)) |
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)) |
(* -1/3 (pow x 2)) |
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3)) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 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))) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* 1/3 (pow x 2)) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(* 4/3 x) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(* 17/9 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(* 17/9 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
| Outputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
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(* 1/3 (pow eps 3)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
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(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
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(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (+ (* eps x) (pow x 2)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))) |
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x)))))))))) |
(* 2/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
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(* 2/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2/3 binary64)) (/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) #s(literal -1/3 binary64)) eps))) |
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 x #s(literal 2/3 binary64)) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) (/.f64 x eps)) #s(literal -1/3 binary64)) eps))) |
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x))) |
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(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(* 2/3 (* (pow eps 4) x)) |
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(* eps x) |
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(* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x))))))) |
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(* 2/3 (pow eps 4)) |
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(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps)))) |
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eps |
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(* eps (+ 1 (* 1/3 (pow eps 2)))) |
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(* eps (+ 1 (* 1/3 (pow eps 2)))) |
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(* 1/3 (pow eps 3)) |
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(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
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(* 1/3 (pow eps 3)) |
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) |
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps eps))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) x)) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) |
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(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
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(* 1/3 (pow eps 2)) |
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(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* 1/3 (pow x 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* 1/3 (pow x 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* 1/3 (pow x 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* 1/3 (pow x 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* 1/3 (pow x 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* x (+ 4/3 (* 17/9 (pow eps 2)))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(+ (* 4/3 x) (* 17/9 (* (pow eps 2) x))) |
(*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))) |
(* 17/9 (* (pow eps 2) x)) |
(*.f64 #s(literal 17/9 binary64) (*.f64 x (*.f64 eps eps))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
(* 17/9 (* (pow eps 2) x)) |
(*.f64 #s(literal 17/9 binary64) (*.f64 x (*.f64 eps eps))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
(* (pow eps 2) (+ (* 4/3 (/ x (pow eps 2))) (* 17/9 x))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps eps)) (*.f64 x #s(literal 17/9 binary64)))) |
Compiled 62740 to 3426 computations (94.5% saved)
28 alts after pruning (25 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 964 | 19 | 983 |
| Fresh | 12 | 6 | 18 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 2 | 2 |
| Total | 980 | 28 | 1008 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 62.3% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ▶ | 61.5% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| 49.7% | (/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) | |
| 62.2% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ▶ | 61.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| ✓ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 97.4% | (+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) | |
| 97.4% | (+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) | |
| 100.0% | (+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)) | |
| 98.7% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) | |
| 99.4% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps) | |
| ▶ | 100.0% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
| 99.8% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) | |
| 98.9% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) | |
| ▶ | 97.4% | (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
| 97.2% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) | |
| 97.4% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) | |
| 98.2% | (*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) | |
| 97.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) | |
| 97.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) | |
| 97.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| 97.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| ▶ | 97.4% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
| 97.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) | |
| ✓ | 97.2% | eps |
Compiled 1635 to 897 computations (45.1% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
| ✓ | cost-diff | 256 | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
| ✓ | cost-diff | 256 | (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
| ✓ | cost-diff | 6784 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (tan.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 256 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| ✓ | cost-diff | 256 | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| ✓ | cost-diff | 256 | (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
| ✓ | cost-diff | 256 | (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
| ✓ | cost-diff | 256 | (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) |
| ✓ | cost-diff | 256 | (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
| ✓ | cost-diff | 19456 | (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))) |
| ✓ | cost-diff | 25792 | (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) |
| ✓ | cost-diff | 25792 | (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) |
| ✓ | cost-diff | 25792 | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
| 2926× | *-lowering-*.f32 |
| 2926× | *-lowering-*.f64 |
| 2872× | +-lowering-+.f64 |
| 2872× | +-lowering-+.f32 |
| 1470× | associate-+r+ |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 60 | 697 |
| 1 | 200 | 635 |
| 2 | 749 | 588 |
| 3 | 3177 | 574 |
| 4 | 7788 | 574 |
| 0 | 8273 | 574 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
eps |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(pow (tan x) 2) |
(tan x) |
x |
2 |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))) |
(+ (tan x) (pow (tan x) 3)) |
(pow (tan x) 3) |
3 |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) |
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(- 1/3 (* (pow (tan x) 2) -1/3)) |
1/3 |
(* (pow (tan x) 2) -1/3) |
-1/3 |
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) |
(+ 1 (pow (tan x) 2)) |
1 |
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))) |
(+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)) |
(* x -1/3) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
(* eps (+ 1 (* x x))) |
eps |
(+ 1 (* x x)) |
1 |
(* x x) |
x |
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps) |
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) |
eps |
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))) |
(* 1/3 (* eps eps)) |
1/3 |
(* eps eps) |
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))) |
x |
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))) |
(* x (+ 1 (* (* eps eps) 4/3))) |
(+ 1 (* (* eps eps) 4/3)) |
1 |
(* (* eps eps) 4/3) |
4/3 |
(* eps (+ 1 (* (* eps eps) 2/3))) |
(+ 1 (* (* eps eps) 2/3)) |
(* (* eps eps) 2/3) |
2/3 |
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) |
(tan (+ x eps)) |
(+ x eps) |
x |
eps |
(/ 1 (/ 1 (tan x))) |
1 |
(/ 1 (tan x)) |
(tan x) |
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x))) |
(/ 1 (cos (+ x eps))) |
1 |
(cos (+ x eps)) |
(+ x eps) |
x |
eps |
(sin (* eps (+ 1 (/ x eps)))) |
(* eps (+ 1 (/ x eps))) |
(+ 1 (/ x eps)) |
(/ x eps) |
(- 0 (tan x)) |
0 |
(tan x) |
| Outputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))))) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)))) |
eps |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))) |
(pow (tan x) 2) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan x) |
(tan.f64 x) |
x |
2 |
#s(literal 2 binary64) |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))))) |
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))) |
(+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))))) |
(+ (tan x) (pow (tan x) 3)) |
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) |
(pow (tan x) 3) |
(pow.f64 (tan.f64 x) #s(literal 3 binary64)) |
3 |
#s(literal 3 binary64) |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))) |
(- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) |
(+.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (+.f64 (*.f64 eps (*.f64 x #s(literal 1/3 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))) |
(+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) |
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(- 1/3 (* (pow (tan x) 2) -1/3)) |
(-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* (pow (tan x) 2) -1/3) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(+ 1 (pow (tan x) 2)) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))) |
(*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 x (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) |
(+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)) |
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 x (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) |
(* x -1/3) |
(*.f64 x #s(literal -1/3 binary64)) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
(* eps (+ 1 (* x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
eps |
(+ 1 (* x x)) |
(+.f64 #s(literal 1 binary64) (*.f64 x x)) |
1 |
#s(literal 1 binary64) |
(* x x) |
(*.f64 x x) |
x |
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x)))))) |
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x))))) |
eps |
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))) |
(+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x)))) |
(* 1/3 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))) |
(*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x))) |
x |
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))) |
(+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))) (+.f64 eps x)) |
(* x (+ 1 (* (* eps eps) 4/3))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
(+ 1 (* (* eps eps) 4/3)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
1 |
#s(literal 1 binary64) |
(* (* eps eps) 4/3) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
4/3 |
#s(literal 4/3 binary64) |
(* eps (+ 1 (* (* eps eps) 2/3))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))))) |
(+ 1 (* (* eps eps) 2/3)) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) |
(* (* eps eps) 2/3) |
(*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) |
2/3 |
#s(literal 2/3 binary64) |
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(tan (+ x eps)) |
(tan.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(/ 1 (/ 1 (tan x))) |
(tan.f64 x) |
1 |
#s(literal 1 binary64) |
(/ 1 (tan x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan x) |
(tan.f64 x) |
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/ 1 (cos (+ x eps))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
1 |
#s(literal 1 binary64) |
(cos (+ x eps)) |
(cos.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(sin (* eps (+ 1 (/ x eps)))) |
(sin.f64 (+.f64 eps x)) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(+ 1 (/ x eps)) |
(+.f64 #s(literal 1 binary64) (/.f64 x eps)) |
(/ x eps) |
(/.f64 x eps) |
(- 0 (tan x)) |
(-.f64 #s(literal 0 binary64) (tan.f64 x)) |
0 |
#s(literal 0 binary64) |
(tan x) |
(tan.f64 x) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (cos.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
| ✓ | accuracy | 93.0% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (tan.f64 x)) |
| ✓ | accuracy | 99.9% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| ✓ | accuracy | 99.8% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 93.1% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| ✓ | accuracy | 99.9% | (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
| ✓ | accuracy | 99.9% | (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
| ✓ | accuracy | 99.9% | (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))) |
| ✓ | accuracy | 99.7% | (*.f64 x #s(literal -1/3 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
| 418.0ms | 147× | 5 | exit |
| 71.0ms | 104× | 0 | valid |
| 7.0ms | 5× | 1 | valid |
Compiled 750 to 60 computations (92% saved)
backward-pass: 97.0ms (35.1% of total)ival-mult: 56.0ms (20.3% of total)ival-add: 31.0ms (11.2% of total)...c/correct-round.rkt:119:19: 24.0ms (8.7% of total)ival-pow: 17.0ms (6.2% of total)ival-tan: 12.0ms (4.3% of total)ival-div: 12.0ms (4.3% of total)ival-sub: 8.0ms (2.9% of total)compiled-spec: 8.0ms (2.9% of total)ival-sin: 7.0ms (2.5% of total)ival-cos: 4.0ms (1.4% of total)const: 1.0ms (0.4% of total)| Inputs |
|---|
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)> |
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))> |
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))> |
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))> |
#<alt (* eps (+ 1 (* x x)))> |
#<alt (+ 1 (* x x))> |
#<alt (* x x)> |
#<alt (+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps)> |
#<alt (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))> |
#<alt (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))> |
#<alt (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))> |
#<alt (- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))> |
#<alt (/ 1 (/ 1 (tan x)))> |
#<alt (tan (+ x eps))> |
#<alt (+ x eps)> |
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x)))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (/ 1 (cos (+ x eps)))> |
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)> |
#<alt (* x -1/3)> |
#<alt (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))> |
#<alt (* (pow (tan x) 2) -1/3)> |
#<alt (* 1/3 (* eps eps))> |
#<alt (* (* eps eps) 2/3)> |
#<alt (* (* eps eps) 4/3)> |
#<alt (/ 1 (tan x))> |
#<alt (cos (+ x eps))> |
| Outputs |
|---|
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))> |
#<alt (* 1/3 (* (pow eps 4) x))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))))> |
#<alt (* 1/3 (* (pow eps 4) x))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))> |
#<alt (* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))> |
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))> |
#<alt (* 1/3 (pow eps 3))> |
#<alt (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))> |
#<alt (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))> |
#<alt (* 1/3 (* (pow eps 4) x))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))> |
#<alt (* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))> |
#<alt (* 1/3 (* (pow eps 4) x))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4)))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2)))))))))))> |
#<alt (* 1/3 (* (pow eps 3) x))> |
#<alt (* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))> |
#<alt (* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))> |
#<alt (* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))> |
#<alt (* 1/3 (* (pow eps 3) x))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3)))))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))> |
#<alt (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
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#<alt (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))> |
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#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))> |
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#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))> |
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#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt eps> |
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#<alt (pow x 2)> |
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#<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)> |
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#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))> |
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#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
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#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))> |
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#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
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#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))> |
#<alt (* 2/3 (* (pow eps 3) x))> |
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#<alt (* 1/3 (pow eps 2))> |
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#<alt (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))))> |
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))> |
#<alt (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))> |
#<alt (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))> |
#<alt (pow x 2)> |
#<alt (+ (* eps x) (pow x 2))> |
#<alt (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2))> |
#<alt (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2))> |
#<alt (* 2/3 (* (pow eps 3) x))> |
#<alt (* (pow eps 3) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))> |
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))> |
#<alt (* 2/3 (* (pow eps 3) x))> |
#<alt (* -1 (* (pow eps 3) (+ (* -4/3 (/ (pow x 2) eps)) (* -2/3 x))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 4/3 (pow x 2)) (/ x eps)) eps)) (* -2/3 x))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))) eps)) (* -2/3 x))))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/3 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin x) (cos x))> |
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- 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 (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))> |
#<alt (- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos 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 (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (cos eps)))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (+ 1 (/ x eps))))> |
#<alt (sin (* eps (- 1 (* -1 (/ x eps)))))> |
#<alt (sin (* eps (- 1 (* -1 (/ x eps)))))> |
#<alt (sin (* eps (- 1 (* -1 (/ x eps)))))> |
#<alt (sin (* eps (- 1 (* -1 (/ x eps)))))> |
#<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 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 (/ 1 (cos eps))> |
#<alt (+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))> |
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))> |
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (- eps (* -1 x))))> |
#<alt (/ 1 (cos (- eps (* -1 x))))> |
#<alt (/ 1 (cos (- eps (* -1 x))))> |
#<alt (/ 1 (cos (- eps (* -1 x))))> |
#<alt (/ 1 (cos x))> |
#<alt (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))> |
#<alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))> |
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (+ eps x)))> |
#<alt (/ 1 (cos (- x (* -1 eps))))> |
#<alt (/ 1 (cos (- x (* -1 eps))))> |
#<alt (/ 1 (cos (- x (* -1 eps))))> |
#<alt (/ 1 (cos (- x (* -1 eps))))> |
#<alt (* -1/3 x)> |
#<alt (* x (- (* -4/9 (pow x 2)) 1/3))> |
#<alt (* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))> |
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* -1/3 x)> |
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))> |
#<alt (* 1/3 eps)> |
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))> |
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))> |
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))> |
#<alt (* 1/3 (* (pow eps 2) x))> |
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))> |
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))> |
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))> |
#<alt (* 1/3 (* (pow eps 2) x))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))> |
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))> |
#<alt (* -1/3 (pow x 2))> |
#<alt (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))> |
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 2/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (* -1/3 (pow x 2))) x)> |
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)> |
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (cos eps)> |
#<alt (+ (cos eps) (* -1 (* x (sin eps))))> |
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))> |
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (- eps (* -1 x)))> |
#<alt (cos (- eps (* -1 x)))> |
#<alt (cos (- eps (* -1 x)))> |
#<alt (cos (- eps (* -1 x)))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (+ eps x))> |
#<alt (cos (- x (* -1 eps)))> |
#<alt (cos (- x (* -1 eps)))> |
#<alt (cos (- x (* -1 eps)))> |
#<alt (cos (- x (* -1 eps)))> |
138 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 2.0ms | x | @ | -inf | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 1.0ms | eps | @ | -inf | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 1.0ms | eps | @ | 0 | (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
| 1.0ms | eps | @ | -inf | (+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x))) |
| 1× | batch-egg-rewrite |
| 2666× | *-lowering-*.f32 |
| 2666× | *-lowering-*.f64 |
| 2170× | fma-lowering-fma.f32 |
| 2170× | fma-lowering-fma.f64 |
| 1920× | fmm-def |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 60 | 444 |
| 1 | 478 | 401 |
| 2 | 5292 | 391 |
| 0 | 8020 | 391 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps) |
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) |
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))) |
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))) |
(* eps (+ 1 (* x x))) |
(+ 1 (* x x)) |
(* x x) |
(+ (* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) eps) |
(* eps (+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))) |
(+ (* 1/3 (* eps eps)) (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))) |
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))) |
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x)))) |
(/ 1 (/ 1 (tan x))) |
(tan (+ x eps)) |
(+ x eps) |
(+ (* (/ 1 (cos (+ x eps))) (sin (* eps (+ 1 (/ x eps))))) (- 0 (tan x))) |
(sin (* eps (+ 1 (/ x eps)))) |
(* eps (+ 1 (/ x eps))) |
(/ 1 (cos (+ x eps))) |
(* (+ (tan x) (pow (tan x) 3)) -1/3) |
(* x -1/3) |
(* eps (- (+ (- 1/3 (* (pow (tan x) 2) -1/3)) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))) |
(* (pow (tan x) 2) -1/3) |
(* 1/3 (* eps eps)) |
(* (* eps eps) 2/3) |
(* (* eps eps) 4/3) |
(/ 1 (tan x)) |
(cos (+ x eps)) |
| Outputs |
|---|
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps) |
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)) eps)) |
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))) eps))) |
(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) eps) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) eps eps) |
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(/.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64)))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) #s(literal -1/3 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) #s(literal -1/3 binary64)) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) |
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) |
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) |
(*.f64 x #s(literal -1/3 binary64)) |
(*.f64 #s(literal -1/3 binary64) x) |
(+.f64 (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) |
(+.f64 (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (*.f64 eps (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) |
(+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps) (*.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) eps)) |
(+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) eps) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) eps)) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 2 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 3 binary64))) eps) (+.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 2 binary64))) eps) (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) |
(*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) |
(*.f64 (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) eps) |
(*.f64 (tan.f64 x) (*.f64 (tan.f64 x) #s(literal -1/3 binary64))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) |
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (tan.f64 x)) |
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 eps #s(literal 1/3 binary64)) eps) |
(*.f64 eps (*.f64 eps #s(literal 2/3 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps #s(literal 2/3 binary64)) eps) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 2/3 binary64)) |
(*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps #s(literal 4/3 binary64)) eps) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 4/3 binary64)) |
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (tan.f64 x) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) |
(+.f64 (cos.f64 (+.f64 eps x)) (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(cos.f64 (+.f64 eps x)) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(-.f64 (/.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 1 binary64))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))) |
(/.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) |
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) |
| 1× | egg-herbie |
| 6400× | +-lowering-+.f64 |
| 6400× | +-lowering-+.f32 |
| 4756× | *-lowering-*.f32 |
| 4756× | *-lowering-*.f64 |
| 1418× | distribute-lft-in |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 813 | 12442 |
| 1 | 2884 | 11993 |
| 0 | 8346 | 11993 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(* 1/3 (* (pow eps 4) x)) |
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
(* 1/3 (* (pow eps 4) x)) |
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) |
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
(* 1/3 (pow eps 3)) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* 1/3 (* (pow eps 4) x)) |
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))) |
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))) |
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x))) |
(* 1/3 (* (pow eps 4) x)) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4))))) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4))))) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)) (* -1/3 (pow eps 4))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2))))))))))) |
(* 1/3 (* (pow eps 3) x)) |
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2)))))) |
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2)))))) |
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2)))))) |
(* 1/3 (* (pow eps 3) x)) |
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3))))) |
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3))))) |
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) x)) (* -1/3 (pow eps 3))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2)))))))))) |
(* 1/3 (* (pow eps 3) x)) |
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
(* 1/3 (* (pow eps 3) x)) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3))))) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3))))) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (pow x 2))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* eps (pow x 2))) |
(+ eps (* eps (pow x 2))) |
(* eps (pow x 2)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* eps (pow x 2)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
1 |
(+ 1 (pow x 2)) |
(+ 1 (pow x 2)) |
(+ 1 (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ 1 (pow x 2)))) |
(* (pow x 2) (+ 1 (/ 1 (pow x 2)))) |
(* (pow x 2) (+ 1 (/ 1 (pow x 2)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ 1 (pow x 2)))) |
(* (pow x 2) (+ 1 (/ 1 (pow x 2)))) |
(* (pow x 2) (+ 1 (/ 1 (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 (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps x) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps))) eps)) (* 2/3 x))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) eps)) (* 2/3 x))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* eps (pow x 2)) |
(* eps (+ (* eps x) (pow x 2))) |
(* eps (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(* eps (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))) |
(* 2/3 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps))) eps)) (* 2/3 x))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x))) |
(* 1/3 (pow eps 3)) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(pow x 2) |
(+ (* eps x) (pow x 2)) |
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)) |
(+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)) |
(* 2/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))) |
(* 2/3 (* (pow eps 3) x)) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x)))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(* eps (* x (+ 1 (* 2/3 (pow eps 2))))) |
(* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 2/3 (pow eps 2)))) x)))) |
(pow x 2) |
(+ (* eps x) (pow x 2)) |
(+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2)) |
(+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2)) |
(* 2/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps)))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))) |
(* 2/3 (* (pow eps 3) x)) |
(* -1 (* (pow eps 3) (+ (* -4/3 (/ (pow x 2) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* 4/3 (pow x 2)) (/ x eps)) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))) eps)) (* -2/3 x)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin x) (cos x)) |
(/ (sin eps) (cos eps)) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/ (sin (- x (* -1 eps))) (cos (- 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))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (- x (* -1 eps)))) (/ (sin x) (cos 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 (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin (* eps (- 1 (* -1 (/ x eps))))) |
(sin (* eps (- 1 (* -1 (/ x eps))))) |
(sin (* eps (- 1 (* -1 (/ x eps))))) |
(sin (* eps (- 1 (* -1 (/ x eps))))) |
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))) |
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))) |
(/ 1 (cos eps)) |
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos (- eps (* -1 x)))) |
(/ 1 (cos x)) |
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))) |
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (+ eps x))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(/ 1 (cos (- x (* -1 eps)))) |
(* -1/3 x) |
(* x (- (* -4/9 (pow x 2)) 1/3)) |
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3)) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* -1/3 x) |
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps)))))) |
(* 1/3 (* (pow eps 2) x)) |
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x))) |
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x))) |
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x))) |
(* 1/3 (* (pow eps 2) x)) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(* -1/3 (pow x 2)) |
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3)) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 1/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 2/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(* 4/3 (pow eps 2)) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (+ eps x)) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
(cos (- x (* -1 eps))) |
| Outputs |
|---|
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)) eps))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
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(+ eps (* 1/3 (pow eps 3))) |
(+.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps)))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))) |
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
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(* 1/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
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(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
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(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) x)))) |
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(* 1/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
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(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
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(* -1 (* x (+ (* -1 (/ (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) x)) (* -1/3 (pow eps 4))))) |
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(/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) |
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))) |
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)) eps))) |
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps)) eps))) |
(* 1/3 (pow eps 3)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 x (*.f64 eps eps)) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/9 binary64))))))))) |
(* 1/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 x) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
(*.f64 (-.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) eps)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))) |
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) |
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))) |
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(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 4/9 (pow eps 2)))))))))) |
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(* 1/3 (* (pow eps 3) x)) |
(*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) x) |
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
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(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
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(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x))) |
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(* 1/3 (* (pow eps 3) x)) |
(*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) x) |
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3))))) |
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(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3))))) |
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(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (+ 1 (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
eps |
(+ eps (* eps (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+ eps (* eps (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+ eps (* eps (pow x 2))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(* eps (pow x 2)) |
(*.f64 eps (*.f64 x x)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x)))) |
(* eps (pow x 2)) |
(*.f64 eps (*.f64 x x)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
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(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x)))) |
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2)))) |
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(* 2/3 (* (pow eps 4) x)) |
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(* 2/3 (* (pow eps 4) x)) |
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) eps)) (* 2/3 x))) |
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(+ eps (* 1/3 (pow eps 3))) |
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))) |
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
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(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
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(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))) |
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
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(* eps (pow x 2)) |
(*.f64 eps (*.f64 x x)) |
(* eps (+ (* eps x) (pow x 2))) |
(*.f64 eps (*.f64 x (+.f64 eps x))) |
(* eps (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) |
(* eps (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))) |
(*.f64 eps (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x)))))))) |
(* 2/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))) |
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(* 2/3 (* (pow eps 4) x)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x))) |
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(* 1/3 (pow eps 3)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))) |
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(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))) |
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))) |
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(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
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(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))) |
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 3) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
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(pow x 2) |
(*.f64 x x) |
(+ (* eps x) (pow x 2)) |
(*.f64 x (+.f64 eps x)) |
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(* 2/3 (* (pow eps 3) x)) |
(*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
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(- (/ (sin (* eps (+ 1 (/ x eps)))) (cos (+ eps x))) (/ (sin x) (cos x))) |
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(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (* eps (- 1 (* -1 (/ x eps))))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(sin x) |
(sin.f64 x) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
(sin eps) |
(sin.f64 eps) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (+ 1 (/ x eps)))) |
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(sin (* eps (- 1 (* -1 (/ x eps))))) |
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(sin (* eps (- 1 (* -1 (/ x eps))))) |
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(sin (* eps (- 1 (* -1 (/ x eps))))) |
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(sin (* eps (- 1 (* -1 (/ x eps))))) |
(sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
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))) |
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(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
eps |
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(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1 binary64))) |
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(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1 binary64))) |
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(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) #s(literal -1 binary64))) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
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(* x (+ 1 (/ eps x))) |
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x |
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(/ 1 (cos eps)) |
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(/ 1 (cos x)) |
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(/ 1 (cos (+ eps x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
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(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) |
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(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))) |
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))) |
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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps)))))) |
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(* 1/3 (* (pow eps 2) x)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 eps eps))) |
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x))) |
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(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x))) |
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(* 1/3 (* (pow eps 2) x)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 eps eps))) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))) x))) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))) x))) |
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)) (/.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))) x))) |
(* -1/3 (pow x 2)) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/9 binary64)) #s(literal -1/3 binary64))) |
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -17/135 binary64)) #s(literal -2/9 binary64))) #s(literal -1/3 binary64))) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3)) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -62/945 binary64)) #s(literal -17/135 binary64))) #s(literal -2/9 binary64))) #s(literal -1/3 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 2/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(/ (cos x) (sin x)) |
(/.f64 (cos.f64 x) (sin.f64 x)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps)) (sin.f64 eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps)))) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x)) (sin.f64 x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
Compiled 36811 to 2548 computations (93.1% saved)
31 alts after pruning (25 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 933 | 12 | 945 |
| Fresh | 7 | 13 | 20 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 942 | 31 | 973 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 62.3% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| ✓ | 61.5% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
| 49.7% | (/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) | |
| 62.2% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 61.5% | (-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x)) | |
| ✓ | 61.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| 61.4% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)))) | |
| ✓ | 62.0% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 97.4% | (+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) | |
| 97.4% | (+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) | |
| 100.0% | (+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)) eps)) | |
| 98.7% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) | |
| 99.4% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps) | |
| 100.0% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps) | |
| 99.8% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) | |
| 98.9% | (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) | |
| 97.4% | (+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) | |
| 97.4% | (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) | |
| 97.2% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) | |
| 97.2% | (+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) | |
| 97.4% | (+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) | |
| 97.4% | (+.f64 (*.f64 eps (*.f64 x x)) eps) | |
| 98.2% | (*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) | |
| 97.4% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| 98.9% | (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| ✓ | 97.4% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
| 97.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) | |
| 6.5% | (*.f64 eps (*.f64 x x)) | |
| ✓ | 97.2% | eps |
Compiled 2841 to 866 computations (69.5% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) |
(/.f64 eps (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) x) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) |
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps) |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps) |
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))) (*.f64 eps eps)) eps)) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (tan.f64 x) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps) |
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps) |
3 calls:
| 37.0ms | x |
| 19.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 16.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) |
(/.f64 eps (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) x) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) |
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps) |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x))))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
3 calls:
| 15.0ms | eps |
| 14.0ms | x |
| 14.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) |
(/.f64 eps (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) x) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) |
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
3 calls:
| 26.0ms | x |
| 13.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
| 98.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) |
(/.f64 eps (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) x) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) |
(*.f64 eps (+.f64 (+.f64 (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 eps #s(literal 4/3 binary64)) (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x)))) |
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
3 calls:
| 15.0ms | eps |
| 12.0ms | x |
| 12.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
| 98.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps) |
(+.f64 (+.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) |
(+.f64 (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (*.f64 (*.f64 eps eps) x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps eps)))) (-.f64 eps (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) (-.f64 (*.f64 x (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))) |
(/.f64 eps (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) x) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps))))) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
3 calls:
| 37.0ms | x |
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) (*.f64 x x))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
2 calls:
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps x)) (*.f64 x x))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
2 calls:
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(+.f64 (*.f64 eps (*.f64 x x)) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
2 calls:
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
Total -58.1b remaining (-3296.6%)
Threshold costs -58.1b (-3296.6%)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 x x)) |
| Outputs |
|---|
eps |
2 calls:
| 4.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.2% | 1 | eps |
| 97.2% | 1 | x |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 700× | distribute-lft-neg-in_binary64 |
| 440× | cancel-sign-sub_binary64 |
| 420× | neg-mul-1_binary64 |
| 398× | unsub-neg_binary64 |
| 328× | neg-sub0_binary64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 74 | 180 |
| 1 | 141 | 179 |
| 2 | 183 | 179 |
| 3 | 218 | 179 |
| 4 | 279 | 179 |
| 5 | 343 | 179 |
| 6 | 497 | 179 |
| 7 | 793 | 179 |
| 8 | 1229 | 179 |
| 9 | 1648 | 179 |
| 10 | 1947 | 179 |
| 11 | 2095 | 179 |
| 12 | 2173 | 179 |
| 13 | 2214 | 179 |
| 14 | 2220 | 179 |
| 15 | 2220 | 179 |
| 16 | 2220 | 179 |
| 1× | saturated |
| Inputs |
|---|
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
eps |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps) |
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 1/3 binary64))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64))))))))))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps) |
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 eps (+.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -2/3 binary64))) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 4/3 binary64))) eps)))) #s(literal 1 binary64))) |
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))))) eps) |
(+.f64 eps (*.f64 eps (+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 4/3 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x)))) eps) |
(+.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 eps x))))) |
(+.f64 (*.f64 eps (*.f64 x (+.f64 eps x))) eps) |
(+.f64 eps (*.f64 eps (*.f64 x (+.f64 eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 (*.f64 x x) #s(literal 1 binary64))) |
eps |
| 6400× | +-lowering-+.f64 |
| 6400× | +-lowering-+.f32 |
| 5576× | *-lowering-*.f32 |
| 5576× | *-lowering-*.f64 |
| 5526× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 850 |
| 1 | 477 | 452 |
| 2 | 5906 | 442 |
| 0 | 8182 | 442 |
| 0 | 939 | 17262 |
| 1 | 3430 | 16961 |
| 0 | 8748 | 16961 |
| 0 | 157 | 1381 |
| 1 | 494 | 1286 |
| 2 | 1891 | 1261 |
| 3 | 7721 | 1261 |
| 0 | 8567 | 1261 |
| 0 | 795 | 15992 |
| 1 | 2801 | 15392 |
| 0 | 8314 | 15392 |
| 0 | 813 | 12442 |
| 1 | 2884 | 11993 |
| 0 | 8346 | 11993 |
| 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 |
Compiled 508 to 257 computations (49.4% saved)
Compiled 404 to 172 computations (57.4% saved)
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