
Time bar (total: 15.7s)
| 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% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 2.9s | 25 541× | 0 | invalid |
| 813.0ms | 5 410× | 0 | valid |
| 547.0ms | 2 846× | 1 | valid |
const: 693.0ms (21.2% of total)ival-tan: 600.0ms (18.3% of total)ival-add: 525.0ms (16% of total)ival-fabs: 371.0ms (11.3% of total)ival-mult: 245.0ms (7.5% of total)ival-sub: 224.0ms (6.8% of total)ival-<=: 201.0ms (6.1% of total)ival-<: 162.0ms (5% of total)ival-and: 101.0ms (3.1% of total)adjust: 94.0ms (2.9% of total)exact: 43.0ms (1.3% of total)ival-assert: 12.0ms (0.4% of total)| 1× | egg-herbie |
| 102× | sub-neg |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 68× | cancel-sign-sub-inv |
| 64× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 221 | 1 | (-5.670654569479482e-178 5.008009389092732e-181) | 2 | (3.225780371294668e-135 3.531463027326352e-137) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3 | 0 | - | 1 | (16.132192673065138 0.6482650219812015) | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | cancellation | 220 | 7 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 2 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 221 | 3 |
| - | 1 | 31 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 221 | 2 | 1 |
| - | 1 | 5 | 26 |
| number | freq |
|---|---|
| 0 | 34 |
| 1 | 222 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 18.0ms | 154× | 1 | valid |
| 17.0ms | 356× | 0 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 58 to 28 computations (51.7% saved)
ival-tan: 9.0ms (40.5% of total)ival-add: 7.0ms (31.5% of total)adjust: 3.0ms (13.5% of total)ival-sub: 3.0ms (13.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.5% | (-.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)) |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 36× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(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 | 99.8% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 63.7% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 11.0ms | 77× | 1 | valid |
| 8.0ms | 178× | 0 | valid |
| 0.0ms | 1× | 3 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 4.0ms (42% of total)adjust: 2.0ms (21% of total)ival-add: 2.0ms (21% of total)ival-sub: 1.0ms (10.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))> |
#<alt (tan.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (tan.f64 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 | |
|---|---|---|---|---|
| 2.0ms | eps | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 2.0ms | eps | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | eps | @ | -inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 1× | batch-egg-rewrite |
| 4 404× | lower-*.f64 |
| 4 404× | lower-*.f32 |
| 3 318× | lower-/.f64 |
| 3 318× | lower-/.f32 |
| 3 264× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(tan.f64 x) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
(+.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(+.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))) |
(+.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)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(-.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 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))) |
(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 x) #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x))) |
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
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(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64)) |
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))) |
(tan.f64 x) |
(neg.f64 (neg.f64 (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 (neg.f64 (sin.f64 x)) (neg.f64 (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 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) #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 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) |
| 1× | egg-herbie |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 5 316× | lower-*.f64 |
| 5 316× | lower-*.f32 |
| 2 664× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 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))) |
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* 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))) |
(fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 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))) |
(fma.f64 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(- (/ (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))))) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(- (/ (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)) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x)) |
(+ (* 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))) |
(fma.f64 x (fma.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 x (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 (sin.f64 eps) (cos.f64 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))) |
(fma.f64 x (fma.f64 x (fma.f64 x (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.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) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (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 (sin.f64 eps) (cos.f64 eps))) |
(/ (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)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(+ (* 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))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (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 (sin.f64 x) (cos.f64 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))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (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 (sin.f64 x) (cos.f64 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 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 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) 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)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
Compiled 8 624 to 983 computations (88.6% saved)
20 alts after pruning (19 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 317 | 19 | 336 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 317 | 20 | 337 |
| Status | Accuracy | Program |
|---|---|---|
| 63.7% | (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 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| 63.7% | (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)) (neg.f64 (tan.f64 x))) | |
| 63.5% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| 98.6% | (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) | |
| ▶ | 98.6% | (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
| ▶ | 98.1% | (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
| 62.6% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 63.5% | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 97.0% | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| 63.5% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) | |
| 63.7% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ▶ | 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| 51.0% | (-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| ▶ | 62.9% | (-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
| 36.0% | (-.f64 (tan.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (tan.f64 x)) | |
| 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| 61.6% | (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) | |
| ▶ | 61.3% | (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
| 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 861 to 440 computations (48.9% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
| ✓ | cost-diff | 0 | (-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
| ✓ | cost-diff | 1408 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
| ✓ | cost-diff | 0 | (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (tan.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 128 | (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
| ✓ | cost-diff | 0 | (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 192 | (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 5824 | (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
| ✓ | cost-diff | 26816 | (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
| 17 934× | lower-fma.f32 |
| 17 920× | lower-fma.f64 |
| 3 970× | lower-*.f32 |
| 3 966× | lower-*.f64 |
| 2 168× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 580 |
| 0 | 88 | 568 |
| 1 | 154 | 498 |
| 2 | 349 | 496 |
| 3 | 916 | 496 |
| 4 | 3434 | 496 |
| 5 | 6137 | 496 |
| 0 | 8102 | 488 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
eps |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
#s(literal 1/6 binary64) |
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
#s(literal 1/3 binary64) |
(*.f64 x x) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(cos.f64 (+.f64 x eps)) |
(tan.f64 x) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
eps |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
| Outputs |
|---|
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(fma.f64 (/.f64 eps (cos.f64 x)) (fma.f64 eps (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (fma.f64 eps (*.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.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 eps eps)) eps)) |
eps |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(fma.f64 eps (+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) |
(+.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) |
#s(literal 1/6 binary64) |
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
#s(literal 1/3 binary64) |
(*.f64 x x) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(tan.f64 (+.f64 eps x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
(+.f64 eps x) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(/.f64 #s(literal 1 binary64) (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(tan.f64 x) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(cos.f64 (+.f64 x eps)) |
(cos.f64 (+.f64 eps x)) |
(tan.f64 x) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
eps |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (cos.f64 (+.f64 x eps)) |
| ✓ | accuracy | 63.7% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| ✓ | accuracy | 99.8% | (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (+.f64 x eps)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
| ✓ | accuracy | 63.7% | (-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
| ✓ | accuracy | 100.0% | (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
| ✓ | accuracy | 99.8% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
| ✓ | accuracy | 64.1% | (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
| ✓ | accuracy | 99.9% | (pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
| ✓ | accuracy | 99.9% | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
| ✓ | accuracy | 99.8% | (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| ✓ | accuracy | 98.5% | (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
| 87.0ms | 171× | 0 | valid |
| 76.0ms | 81× | 1 | valid |
| 57.0ms | 3× | 5 | exit |
| 2.0ms | 1× | 3 | valid |
Compiled 604 to 54 computations (91.1% saved)
ival-tan: 56.0ms (29.5% of total)ival-add: 46.0ms (24.2% of total)ival-div: 17.0ms (9% of total)ival-mult: 15.0ms (7.9% of total)adjust: 13.0ms (6.9% of total)ival-pow: 10.0ms (5.3% of total)const: 8.0ms (4.2% of total)ival-pow2: 6.0ms (3.2% of total)ival-cos: 6.0ms (3.2% of total)ival-sin: 6.0ms (3.2% of total)ival-sub: 5.0ms (2.6% of total)exact: 1.0ms (0.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))> |
#<alt (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)> |
#<alt (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))> |
#<alt (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))> |
#<alt (-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x))> |
#<alt (tan.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)> |
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))> |
#<alt (-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))> |
#<alt (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))))> |
#<alt (/.f64 #s(literal 1 binary64) (+.f64 x eps))> |
#<alt (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))> |
#<alt (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)> |
#<alt (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))> |
#<alt (pow.f64 (sin.f64 x) #s(literal 2 binary64))> |
#<alt (sin.f64 x)> |
#<alt (pow.f64 (sin.f64 x) #s(literal 4 binary64))> |
#<alt (pow.f64 (sin.f64 x) #s(literal 3 binary64))> |
#<alt (*.f64 #s(literal 1/3 binary64) (*.f64 x x))> |
#<alt (cos.f64 (+.f64 x eps))> |
#<alt (pow.f64 (cos.f64 x) #s(literal 2 binary64))> |
#<alt (cos.f64 x)> |
| Outputs |
|---|
#<alt -1/2> |
#<alt (- (* -1/3 (pow x 2)) 1/2)> |
#<alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)> |
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)> |
#<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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 -1/3> |
#<alt (- (* -1/3 (pow x 2)) 1/3)> |
#<alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/3)> |
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3)> |
#<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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* (pow eps 2) (- (+ 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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (/ (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))> |
#<alt (* -1 (* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 3) (- (/ (sin (+ eps x)) (* (pow x 3) (cos (+ eps x)))) (+ 1/3 (/ 1 (pow x 2)))))> |
#<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))> |
#<alt (* -1 (* (pow x 3) (+ 1/3 (/ 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 (* -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 (* 1/3 (pow x 3))))> |
#<alt (- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (+ x (* 1/3 (pow x 3))))> |
#<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 (* 1/3 (pow x 3))))> |
#<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 (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3))))> |
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3))))> |
#<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 (* 1/3 (pow x 2))))> |
#<alt (* x (+ 1 (* 1/3 (pow x 2))))> |
#<alt (* 1/3 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<alt (* 1/3 (pow x 3))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))> |
#<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 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 (/ 1 eps)> |
#<alt (+ (* -1 (/ x (pow eps 2))) (/ 1 eps))> |
#<alt (+ (* x (- (/ x (pow eps 3)) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (* -1 (/ eps x))) x)> |
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (/ eps x)) x)> |
#<alt (/ (- (+ 1 (* -1 (/ (pow eps 3) (pow x 3)))) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (/ eps x) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) eps) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow eps 3) x) (pow eps 2)) x)) eps) x)) 1) x))> |
#<alt (/ 1 x)> |
#<alt (+ (* -1 (/ eps (pow x 2))) (/ 1 x))> |
#<alt (+ (* eps (- (/ eps (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))> |
#<alt (+ (* eps (- (* eps (+ (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))> |
#<alt (/ 1 eps)> |
#<alt (/ (+ 1 (* -1 (/ x eps))) eps)> |
#<alt (/ (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)) eps)> |
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow eps 3)))) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))) eps)> |
#<alt (/ 1 eps)> |
#<alt (* -1 (/ (- (/ x eps) 1) eps))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) eps) x) eps)) 1) eps))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (pow x 2)) eps)) x) eps)) 1) 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 (/ (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 (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)> |
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#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))> |
#<alt eps> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))> |
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (pow x 2)> |
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#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt (pow (sin x) 2)> |
#<alt x> |
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#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (pow x 4)> |
#<alt (* (pow x 4) (+ 1 (* -2/3 (pow x 2))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow (sin x) 4)> |
#<alt (pow x 3)> |
#<alt (* (pow x 3) (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))> |
#<alt (* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<alt (pow (sin x) 3)> |
#<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 (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)))> |
#<alt 1> |
#<alt (+ 1 (* -1 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
117 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | eps | @ | inf | (+ (* eps (/ (pow (sin x) 2) (pow (cos x) 2))) eps) |
| 8.0ms | x | @ | inf | (+ (* eps (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 7.0ms | x | @ | inf | (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
| 5.0ms | x | @ | -inf | (+ (* eps (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 3.0ms | x | @ | inf | (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2)) |
| 1× | batch-egg-rewrite |
| 4 156× | lower-*.f32 |
| 4 152× | lower-*.f64 |
| 3 934× | lower-fma.f32 |
| 3 920× | lower-fma.f64 |
| 3 218× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 331 |
| 0 | 88 | 309 |
| 1 | 418 | 217 |
| 2 | 3681 | 213 |
| 0 | 8180 | 205 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 x eps)) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(cos.f64 (+.f64 x eps)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
| Outputs |
|---|
(+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) |
(+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) |
(+.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) |
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1/6 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) |
(/.f64 (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) |
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(/.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
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(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 x))) |
(*.f64 (sin.f64 x) (sin.f64 x)) |
(exp.f64 (log.f64 (sin.f64 x))) |
(sin.f64 x) |
(pow.f64 (sin.f64 x) #s(literal 1 binary64)) |
(pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 #s(literal 4 binary64) (log.f64 (sin.f64 x)))) |
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 #s(literal 3 binary64) (log.f64 (sin.f64 x))))) |
(exp.f64 (fma.f64 #s(literal 3 binary64) (log.f64 (sin.f64 x)) (log.f64 (sin.f64 x)))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 (sin.f64 x))) |
(*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) |
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (sin.f64 x)) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 4 binary64))) |
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 (sin.f64 x)))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) #s(literal 3/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))))) |
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x)) (log.f64 (sin.f64 x)))) |
(exp.f64 (fma.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64) (*.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64)))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (sin.f64 x))) |
(*.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x)) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 3 binary64))) |
(*.f64 x (*.f64 x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 x #s(literal 1/3 binary64)) x) |
(+.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))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(cos.f64 (+.f64 x eps)) |
(cos.f64 (neg.f64 (+.f64 x eps))) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1 binary64) x)) (cos.f64 (*.f64 #s(literal 1 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 #s(literal 1 binary64) eps)))) |
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1 binary64) eps)) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (sin.f64 (*.f64 #s(literal 1 binary64) eps)) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal 1 binary64))) (cos.f64 (*.f64 eps #s(literal 1 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal 1 binary64))) (sin.f64 (*.f64 eps #s(literal 1 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1 binary64))) (cos.f64 (*.f64 x #s(literal 1 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1 binary64))) (sin.f64 (*.f64 x #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 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(/.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 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 x eps))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x)))) |
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))) #s(literal 1 binary64))) |
(exp.f64 (+.f64 (log.f64 (cos.f64 x)) (log.f64 (cos.f64 x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) (cos.f64 (-.f64 x x))) #s(literal 2 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 x))) |
(*.f64 (cos.f64 x) (cos.f64 x)) |
(exp.f64 (log.f64 (cos.f64 x))) |
(cos.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 1 binary64)) |
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x))) |
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64))) |
| 1× | egg-herbie |
| 7 972× | lower-fma.f64 |
| 7 972× | lower-fma.f32 |
| 6 056× | lower-*.f64 |
| 6 056× | lower-*.f32 |
| 3 254× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 594 | 8175 |
| 1 | 1794 | 7938 |
| 2 | 5636 | 7788 |
| 0 | 8437 | 7427 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/2 |
(- (* -1/3 (pow x 2)) 1/2) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))) 1/2) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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)))) 1/2) |
(* 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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))))) |
-1/3 |
(- (* -1/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 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) (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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ 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) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))) |
(/ (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 (* 1/3 (pow x 3)))) |
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (+ x (* 1/3 (pow x 3)))) |
(- (+ (* 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 (* 1/3 (pow x 3)))) |
(- (+ (* 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 (* 1/3 (pow x 3)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (+ x (* 1/3 (pow x 3)))) |
(/ (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 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* 1/3 (pow x 3)) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(* 1/3 (pow x 3)) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
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))) |
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(- (/ (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)))) |
(/ 1 eps) |
(+ (* -1 (/ x (pow eps 2))) (/ 1 eps)) |
(+ (* x (- (/ x (pow eps 3)) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(+ (* x (- (* x (+ (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(/ 1 x) |
(/ (+ 1 (* -1 (/ eps x))) x) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (/ eps x)) x) |
(/ (- (+ 1 (* -1 (/ (pow eps 3) (pow x 3)))) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))) x) |
(/ 1 x) |
(* -1 (/ (- (/ eps x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) eps) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow eps 3) x) (pow eps 2)) x)) eps) x)) 1) x)) |
(/ 1 x) |
(+ (* -1 (/ eps (pow x 2))) (/ 1 x)) |
(+ (* eps (- (/ eps (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) |
(+ (* eps (- (* eps (+ (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(/ 1 eps) |
(/ (+ 1 (* -1 (/ x eps))) eps) |
(/ (- (+ 1 (/ (pow x 2) (pow eps 2))) (/ x eps)) eps) |
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow eps 3)))) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))) eps) |
(/ 1 eps) |
(* -1 (/ (- (/ x eps) 1) eps)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) eps) x) eps)) 1) eps)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (pow x 2)) eps)) x) eps)) 1) 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))) |
(/ (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)))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
(pow (sin x) 2) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow (sin x) 4) |
(pow x 3) |
(* (pow x 3) (+ 1 (* -1/2 (pow x 2)))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2)))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2)))) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(pow (sin x) 3) |
(* 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)) |
(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))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
| Outputs |
|---|
-1/2 |
#s(literal -1/2 binary64) |
(- (* -1/3 (pow x 2)) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) |
(fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/9 binary64) #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -17/135 binary64) #s(literal -2/9 binary64))) #s(literal -1/3 binary64)) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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)))) 1/2) |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (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) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (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))))) |
(fma.f64 eps (fma.f64 eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (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) |
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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eps |
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(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
x |
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(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
x |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* 1/3 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* 1/3 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64))) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* (pow x 3) (+ 1/3 (/ 1 (pow x 2)))) |
(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
eps |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
x |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
(+ eps x) |
(+.f64 x eps) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* 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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(* 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))))) |
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.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))) |
(fma.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)))) (/.f64 (sin.f64 eps) (cos.f64 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))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
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(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ (sin eps) (cos eps)) |
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(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (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)) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
(+ (* 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))) |
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 eps (*.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 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))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 x (cos.f64 eps) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps)) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 eps) (*.f64 (*.f64 x (cos.f64 eps)) #s(literal -1/6 binary64))) (cos.f64 eps)) (sin.f64 eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 x eps)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (*.f64 eps #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 eps #s(literal 2/45 binary64) (fma.f64 #s(literal -1/3 binary64) eps (*.f64 eps #s(literal 2/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))) eps) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 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 (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 (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 (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 (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 (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 (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 (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64))) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(pow x 4) |
(*.f64 (*.f64 x x) (*.f64 x x)) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal -2/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/5 binary64) #s(literal -2/3 binary64))) #s(literal 1 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -34/945 binary64) #s(literal 1/5 binary64)) #s(literal -2/3 binary64)) #s(literal 1 binary64))) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* (pow x 3) (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 (*.f64 x x) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 13/120 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -41/3024 binary64) #s(literal 13/120 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(pow (sin x) 3) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(* 1/3 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal 1/3 binary64)) |
(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)))) |
(fma.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))) (neg.f64 (sin.f64 eps))) (cos.f64 eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 eps (-.f64 (*.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))) (cos.f64 x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (pow x 2))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
Compiled 87 130 to 5 150 computations (94.1% saved)
27 alts after pruning (25 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 841 | 19 | 1 860 |
| Fresh | 8 | 6 | 14 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 853 | 27 | 1 880 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 98.6% | (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
| 98.1% | (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) | |
| 63.7% | (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)) (neg.f64 (tan.f64 x))) | |
| 97.6% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) | |
| 96.8% | (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) | |
| 63.5% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) | |
| ▶ | 97.4% | (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
| 97.5% | (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| 96.9% | (fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| 98.6% | (fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) | |
| ▶ | 97.6% | (fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
| 97.8% | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) | |
| 97.7% | (fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) | |
| ▶ | 97.4% | (fma.f64 eps (*.f64 x x) eps) |
| 30.0% | (/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) | |
| 62.6% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 63.7% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 36.1% | (-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| ✓ | 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| ▶ | 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
| 51.0% | (-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| 62.9% | (-.f64 (tan.f64 (fma.f64 eps (/.f64 x eps) eps)) (tan.f64 x)) | |
| 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 98.1% | (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) | |
| 5.8% | (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
Compiled 1 051 to 564 computations (46.3% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
| ✓ | cost-diff | 1728 | (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
| ✓ | cost-diff | 7168 | (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
| ✓ | cost-diff | 0 | (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
| ✓ | cost-diff | 192 | (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (fma.f64 eps (*.f64 x x) eps) |
| ✓ | cost-diff | 128 | (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| ✓ | cost-diff | 6272 | (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
| ✓ | cost-diff | 13056 | (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
| 11 914× | lower-fma.f32 |
| 11 890× | lower-fma.f64 |
| 4 972× | lower-*.f32 |
| 4 956× | lower-*.f64 |
| 2 416× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 583 |
| 0 | 109 | 573 |
| 1 | 216 | 547 |
| 2 | 524 | 544 |
| 3 | 1457 | 511 |
| 4 | 3475 | 511 |
| 5 | 5983 | 501 |
| 0 | 8865 | 487 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
#s(literal 1/2 binary64) |
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(cos.f64 x) |
(fma.f64 eps (*.f64 x x) eps) |
eps |
(*.f64 x x) |
x |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
eps |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
x |
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
eps |
(/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 x x) |
x |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
#s(literal 1 binary64) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(-.f64 x eps) |
#s(literal -1 binary64) |
(/.f64 #s(literal 1 binary64) (-.f64 x eps)) |
(tan.f64 x) |
| Outputs |
|---|
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) |
(-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) |
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)) |
(/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (cos.f64 x)) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(cos.f64 x) |
(fma.f64 eps (*.f64 x x) eps) |
eps |
(*.f64 x x) |
x |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (+.f64 eps x) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))) eps) |
eps |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(fma.f64 x (+.f64 eps x) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))) |
x |
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 (*.f64 x x) (/.f64 (fma.f64 eps (*.f64 #s(literal -1/3 binary64) (*.f64 x x)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
eps |
(/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(*.f64 (*.f64 x x) (/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 x x) |
x |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
#s(literal -1/3 binary64) |
#s(literal 1 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(cos.f64 (+.f64 eps x)) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(+.f64 eps x) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) |
(*.f64 (+.f64 eps x) (-.f64 x eps)) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps))) |
#s(literal 1 binary64) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(*.f64 (+.f64 eps x) (-.f64 x eps)) |
(-.f64 x eps) |
#s(literal -1 binary64) |
(/.f64 #s(literal 1 binary64) (-.f64 x eps)) |
(tan.f64 x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (-.f64 x eps)) |
| ✓ | accuracy | 98.6% | (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) |
| ✓ | accuracy | 63.7% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
| ✓ | accuracy | 55.1% | (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
| ✓ | accuracy | 100.0% | (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
| ✓ | accuracy | 100.0% | (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
| ✓ | accuracy | 99.8% | (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (fma.f64 eps (*.f64 x x) eps) |
| ✓ | accuracy | 100.0% | (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
| ✓ | accuracy | 99.8% | (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
| ✓ | accuracy | 56.1% | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| 265.0ms | 240× | 1 | valid |
| 9.0ms | 3× | 5 | exit |
| 6.0ms | 12× | 0 | valid |
| 3.0ms | 1× | 3 | valid |
Compiled 617 to 67 computations (89.1% saved)
ival-cos: 52.0ms (21.9% of total)ival-mult: 51.0ms (21.5% of total)adjust: 35.0ms (14.7% of total)ival-add: 32.0ms (13.5% of total)ival-div: 18.0ms (7.6% of total)ival-pow2: 13.0ms (5.5% of total)const: 13.0ms (5.5% of total)ival-sub: 8.0ms (3.4% of total)ival-sin: 8.0ms (3.4% of total)ival-pow: 5.0ms (2.1% of total)ival-tan: 3.0ms (1.3% of total)exact: 1.0ms (0.4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))> |
#<alt (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))> |
#<alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))> |
#<alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))> |
#<alt (fma.f64 eps (*.f64 x x) eps)> |
#<alt (*.f64 x x)> |
#<alt (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))> |
#<alt (fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)> |
#<alt (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)> |
#<alt (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))> |
#<alt (fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)> |
#<alt (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))> |
#<alt (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)))> |
#<alt (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64))> |
#<alt (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))> |
#<alt (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x))> |
#<alt (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))))> |
#<alt (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))> |
#<alt (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))> |
#<alt (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))> |
#<alt (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))> |
#<alt (pow.f64 (cos.f64 x) #s(literal 2 binary64))> |
#<alt (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))> |
#<alt (/.f64 #s(literal 1 binary64) (-.f64 x eps))> |
| Outputs |
|---|
#<alt (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))> |
#<alt (* 1/3 eps)> |
#<alt (+ x (* 1/3 eps))> |
#<alt (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))> |
#<alt (+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))> |
#<alt x> |
#<alt (* x (+ 1 (* 5/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))> |
#<alt (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))> |
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (- 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (- 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (- 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (- 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))> |
#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* -1 (* eps (- (* -1 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (pow x 2)) 1)))> |
#<alt eps> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (* eps (pow x 2))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (* eps (pow x 2))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 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 x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))> |
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))> |
#<alt (pow x 2)> |
#<alt (+ (* eps x) (pow x 2))> |
#<alt (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))> |
#<alt (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))> |
#<alt (* eps (+ 1 (pow x 2)))> |
#<alt (* eps (+ 1 (+ (* eps x) (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps)))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))> |
#<alt (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))> |
#<alt (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))> |
#<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) x)))))> |
#<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) x)))))> |
#<alt (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))> |
#<alt (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))> |
#<alt eps> |
#<alt (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))> |
#<alt (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))> |
#<alt (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))> |
#<alt (* x (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))> |
#<alt (* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))> |
#<alt (* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))> |
#<alt (* x (+ 1 (* 4/3 (pow eps 2))))> |
#<alt (* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x)))))> |
#<alt (* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x)))))> |
#<alt (* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x)))))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ x (* eps (+ 1 (* 4/3 (* eps x)))))> |
#<alt (+ x (* eps (+ 1 (* 4/3 (* eps x)))))> |
#<alt (* 4/3 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))> |
#<alt (* 4/3 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))> |
#<alt 1> |
#<alt (+ 1 (* 4/3 (pow eps 2)))> |
#<alt (+ 1 (* 4/3 (pow eps 2)))> |
#<alt (+ 1 (* 4/3 (pow eps 2)))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* 4/3 (pow eps 2))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))))> |
#<alt (* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1)))> |
#<alt eps> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))> |
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps)))) (* -1/3 eps)) (* -1 eps))))))> |
#<alt (* -1/3 (/ (* eps (pow x 4)) (pow (cos x) 2)))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (/ eps (* (pow x 2) (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4)))))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4)))))> |
#<alt (* -1/3 (/ (* eps (pow x 4)) (pow (cos x) 2)))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (/ eps (* (pow x 2) (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4)))))> |
#<alt (* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 1/3 (pow x 2))))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 1/3 (* 7/45 (pow x 2))))))))> |
#<alt (* -1/3 (/ (pow x 4) (pow (cos x) 2)))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (* -1/3 (/ (pow x 4) (pow (cos x) 2)))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* -1/3 (pow x 4))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* -1/3 (pow x 4))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 4) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* -1 (pow eps 2))> |
#<alt (+ (* -1 (pow eps 2)) (* x (+ eps (* -1 eps))))> |
#<alt (+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps)))))> |
#<alt (+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x)))))> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x))))> |
#<alt (pow x 2)> |
#<alt (+ (* eps (+ x (* -1 x))) (pow x 2))> |
#<alt (+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2))> |
#<alt (+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2))> |
#<alt (* -1 (pow eps 2))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ x eps)) 1))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1))> |
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1))> |
#<alt (* -1 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (* -1 x)) eps)) 1))> |
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1))> |
#<alt (* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) 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 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 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 (pow x 4)> |
#<alt (* (pow x 4) (+ 1 (* 1/3 (pow x 2))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2))))))))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 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 1> |
#<alt (+ 1 (* -1 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt (pow (cos x) 2)> |
#<alt 1> |
#<alt (+ 1 (* -1/3 (pow x 2)))> |
#<alt (+ 1 (* -1/3 (pow x 2)))> |
#<alt (+ 1 (* -1/3 (pow x 2)))> |
#<alt (* -1/3 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* -1/3 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/3))> |
#<alt (/ -1 eps)> |
#<alt (- (* -1 (/ x (pow eps 2))) (/ 1 eps))> |
#<alt (- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (/ eps x)) x)> |
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)> |
#<alt (/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (* -1 (/ eps x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))> |
#<alt (/ 1 x)> |
#<alt (+ (/ 1 x) (/ eps (pow x 2)))> |
#<alt (+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))> |
#<alt (+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))> |
#<alt (/ -1 eps)> |
#<alt (/ (- (* -1 (/ x eps)) 1) eps)> |
#<alt (/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)> |
#<alt (/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)> |
#<alt (/ -1 eps)> |
#<alt (* -1 (/ (+ 1 (/ x eps)) eps))> |
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))> |
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | eps | @ | 0 | (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) |
| 10.0ms | x | @ | -inf | (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) |
| 5.0ms | x | @ | inf | (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) |
| 3.0ms | x | @ | -inf | (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) |
| 3.0ms | x | @ | inf | (+ (* eps (+ (* eps (- (/ (+ (- 1/2 (* 1/2 (cos (+ x x)))) (pow (* (sin x) (tan x)) 2)) (+ 1/2 (* 1/2 (cos (+ x x))))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x)))) (pow (tan x) 2)) |
| 1× | batch-egg-rewrite |
| 4 574× | lower-fma.f32 |
| 4 552× | lower-fma.f64 |
| 4 544× | lower-*.f32 |
| 4 528× | lower-*.f64 |
| 3 102× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 52 | 356 |
| 0 | 106 | 354 |
| 1 | 482 | 278 |
| 2 | 4172 | 265 |
| 0 | 8533 | 262 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) |
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 eps (*.f64 x x) eps) |
(*.f64 x x) |
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (-.f64 x eps)) |
| Outputs |
|---|
(+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(+.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))) (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))))) |
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(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) |
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 (+.f64 x x)))))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) (neg.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64))) |
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 x))) |
(*.f64 (cos.f64 x) (cos.f64 x)) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) |
(*.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x)))))))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x))) |
(+.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) |
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))) |
(fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal -1/3 binary64) (*.f64 x x))))) |
(/.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)))) |
(pow.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/27 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 x x)))))) |
(*.f64 (fma.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))) |
(exp.f64 (*.f64 (log.f64 (-.f64 x eps)) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (-.f64 x eps)) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 x eps))) |
(pow.f64 (-.f64 x eps) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (-.f64 x eps))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (-.f64 x eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (-.f64 x eps) (-.f64 x eps)) #s(literal -1/2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (-.f64 x eps))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 eps x)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1/2 binary64)) (pow.f64 (-.f64 x eps) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 eps x) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (-.f64 x eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 eps x) (*.f64 x x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
| 1× | egg-herbie |
| 8 808× | lower-fma.f64 |
| 8 808× | lower-fma.f32 |
| 5 250× | lower-*.f64 |
| 5 250× | lower-*.f32 |
| 4 584× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 664 | 8261 |
| 1 | 2174 | 8028 |
| 2 | 6814 | 7832 |
| 0 | 8326 | 7329 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
(* 1/3 eps) |
(+ x (* 1/3 eps)) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(* 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))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
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)))) |
(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) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* 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 x)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 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 (* 4/3 (pow x 2)))))) (pow x 2)) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (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 (* 4/3 (pow x 2)))))) (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (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) 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) 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) x))))) |
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))))) |
x |
(+ eps x) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x))) |
1 |
(+ 1 (* 4/3 (pow eps 2))) |
(+ 1 (* 4/3 (pow eps 2))) |
(+ 1 (* 4/3 (pow eps 2))) |
(* 4/3 (pow eps 2)) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* 4/3 (pow eps 2)) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* eps (+ 1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2)))) |
(* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1))) |
(* -1 (* eps (- (* -1 (/ (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (pow (cos x) 2))) 1))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps)))) (* -1/3 eps)) (* -1 eps)))))) |
(* -1/3 (/ (* eps (pow x 4)) (pow (cos x) 2))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (/ eps (* (pow x 2) (pow (cos x) 2))))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4))))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4))))) |
(* -1/3 (/ (* eps (pow x 4)) (pow (cos x) 2))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (/ eps (* (pow x 2) (pow (cos x) 2))))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4))))) |
(* (pow x 4) (+ (* -1/3 (/ eps (pow (cos x) 2))) (+ (/ eps (* (pow x 2) (pow (cos x) 2))) (/ eps (pow x 4))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 1/3 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 1/3 (* 7/45 (pow x 2)))))))) |
(* -1/3 (/ (pow x 4) (pow (cos x) 2))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(* -1/3 (/ (pow x 4) (pow (cos x) 2))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(* (pow x 4) (- (/ 1 (* (pow x 2) (pow (cos x) 2))) (* 1/3 (/ 1 (pow (cos x) 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* -1/3 (pow x 4)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* -1/3 (pow x 4)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 4) (- (/ 1 (pow x 2)) 1/3)) |
(* -1 (pow eps 2)) |
(+ (* -1 (pow eps 2)) (* x (+ eps (* -1 eps)))) |
(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps))))) |
(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) |
(pow x 2) |
(+ (* eps (+ x (* -1 x))) (pow x 2)) |
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) |
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) |
(* -1 (pow eps 2)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ x eps)) 1)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1)) |
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1)) |
(* -1 (pow eps 2)) |
(* (pow eps 2) (- (* -1 (/ (+ x (* -1 x)) eps)) 1)) |
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1)) |
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) 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))) |
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 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)))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* (pow eps 2) (- (+ 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)) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 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 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 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)) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
(pow (cos x) 2) |
1 |
(+ 1 (* -1/3 (pow x 2))) |
(+ 1 (* -1/3 (pow x 2))) |
(+ 1 (* -1/3 (pow x 2))) |
(* -1/3 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(* -1/3 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(/ -1 eps) |
(- (* -1 (/ x (pow eps 2))) (/ 1 eps)) |
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(/ 1 x) |
(/ (+ 1 (/ eps x)) x) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x) |
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x) |
(/ 1 x) |
(* -1 (/ (- (* -1 (/ eps x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x)) |
(/ 1 x) |
(+ (/ 1 x) (/ eps (pow x 2))) |
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x)) |
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(/ -1 eps) |
(/ (- (* -1 (/ x eps)) 1) eps) |
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps) |
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps) |
(/ -1 eps) |
(* -1 (/ (+ 1 (/ x eps)) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps)) |
| Outputs |
|---|
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
(fma.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) |
(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ x (* 1/3 eps)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
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(fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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(+ (* eps (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) |
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x |
(* x (+ 1 (* 5/6 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal 5/6 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 277/1008 binary64) #s(literal 61/120 binary64)) #s(literal 5/6 binary64)) x) x) |
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) |
(+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(*.f64 x (*.f64 x (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (pow x 2))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (* 2 x)))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/2 (cos (neg (* -2 x))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(fma.f64 x (*.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(fma.f64 x (*.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(fma.f64 x (*.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (pow x 2)) 1))) |
(fma.f64 x (*.f64 x eps) eps) |
eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (pow x 2)) |
(*.f64 x (*.f64 x eps)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(* eps (pow x 2)) |
(*.f64 x (*.f64 x eps)) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ eps (/ eps (pow x 2)))) |
(*.f64 x (*.f64 x (+.f64 eps (/.f64 eps (*.f64 x x))))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* 1/3 (pow eps 2)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(*.f64 x (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) x)) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(*.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x)) x)) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(*.f64 (*.f64 x x) (+.f64 (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps (/.f64 eps (*.f64 x x))) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(*.f64 (*.f64 x x) (+.f64 (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps (/.f64 eps (*.f64 x x))) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(*.f64 x (fma.f64 x (*.f64 eps (*.f64 eps #s(literal 4/3 binary64))) x)) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(*.f64 x (fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) (/.f64 eps x)) x)) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 x x) (-.f64 (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 eps eps) x) (neg.f64 eps)) x))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2))))) |
(*.f64 (*.f64 x x) (-.f64 (fma.f64 eps (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 eps eps) x) (neg.f64 eps)) x))) |
(pow x 2) |
(*.f64 x x) |
(+ (* eps x) (pow x 2)) |
(*.f64 x (+.f64 x eps)) |
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)) |
(fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) |
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)) |
(fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (+.f64 #s(literal 1/3 binary64) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (+.f64 #s(literal 1/3 binary64) (/.f64 x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) (+.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)))) |
(* eps (+ 1 (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(* eps (+ 1 (+ (* eps x) (pow x 2)))) |
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(fma.f64 x (/.f64 eps x) x) |
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(/ (sin eps) (cos eps)) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (-.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 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)) |
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(pow x 2) |
(*.f64 x x) |
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(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (* 2 x)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (- (+ 1/2 (/ (pow (sin x) 4) (pow (cos x) 2))) (* 1/2 (cos (neg (* -2 x))))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (fma.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 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)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (pow x 2))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/3 (pow x 2))) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1/3 (pow x 2))) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* -1/3 (pow x 2))) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* -1/3 (pow x 2)) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x x)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* -1/3 (pow x 2)) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x x)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3)) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) |
(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(- (* -1 (/ x (pow eps 2))) (/ 1 eps)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps) |
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(fma.f64 x (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps eps)) (/.f64 x (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) eps)) |
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(fma.f64 x (fma.f64 x (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 x (pow.f64 eps #s(literal 4 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1 binary64) eps)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ (+ 1 (/ eps x)) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 eps x) eps) x)) x) |
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (+.f64 (fma.f64 (*.f64 eps eps) (/.f64 eps (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (fma.f64 eps (/.f64 eps x) eps) x)) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(* -1 (/ (- (* -1 (/ eps x)) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x) |
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 eps x) eps) x)) x) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x)) |
(/.f64 (+.f64 (/.f64 (+.f64 eps (/.f64 (fma.f64 eps (/.f64 (*.f64 eps eps) x) (*.f64 eps eps)) x)) x) #s(literal 1 binary64)) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(+ (/ 1 x) (/ eps (pow x 2))) |
(+.f64 (/.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) |
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x)) |
(+.f64 (/.f64 eps (*.f64 x x)) (fma.f64 eps (/.f64 eps (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))) |
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(fma.f64 eps (fma.f64 eps (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 eps (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))) |
(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(/ (- (* -1 (/ x eps)) 1) eps) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps) |
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)) (neg.f64 eps)) |
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps) |
(/.f64 (-.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (/.f64 x eps) x) eps))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) eps) |
(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(* -1 (/ (+ 1 (/ x eps)) eps)) |
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 x eps)) eps) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (/.f64 x eps) x) eps)) (neg.f64 eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (fma.f64 x x (*.f64 x (/.f64 (*.f64 x x) eps))) eps) x) eps)) (neg.f64 eps)) |
Compiled 40 532 to 3 486 computations (91.4% saved)
32 alts after pruning (29 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 058 | 18 | 1 076 |
| Fresh | 9 | 11 | 20 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 071 | 32 | 1 103 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 98.6% | (fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
| 97.5% | (fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) | |
| 96.9% | (fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) | |
| 98.2% | (fma.f64 (fma.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.6% | (fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.2% | (fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.6% | (fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.1% | (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) | |
| 97.6% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) | |
| 96.8% | (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) | |
| 97.4% | (fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| 97.4% | (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) | |
| 97.7% | (fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) | |
| ▶ | 97.8% | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
| 97.7% | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) | |
| ▶ | 96.8% | (fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
| 97.4% | (fma.f64 eps (*.f64 x (+.f64 x eps)) eps) | |
| 97.7% | (fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) | |
| 97.7% | (fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) | |
| ✓ | 97.4% | (fma.f64 eps (*.f64 x x) eps) |
| 63.7% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 36.1% | (-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) | |
| ✓ | 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) | |
| 51.0% | (-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| ▶ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 97.4% | (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) | |
| 98.1% | (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) | |
| ▶ | 6.5% | (*.f64 x (*.f64 x eps)) |
| 5.8% | (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
Compiled 1 187 to 658 computations (44.6% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 (sin.f64 x) (cos.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)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
| ✓ | cost-diff | 0 | (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 eps eps) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
| ✓ | cost-diff | 0 | (*.f64 x eps) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
| ✓ | cost-diff | 0 | (fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
| ✓ | cost-diff | 13056 | (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
| 10 406× | lower-fma.f32 |
| 10 382× | lower-fma.f64 |
| 3 494× | lower-*.f32 |
| 3 474× | lower-*.f64 |
| 3 192× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 50 | 468 |
| 0 | 100 | 468 |
| 1 | 191 | 467 |
| 2 | 501 | 465 |
| 3 | 1467 | 456 |
| 4 | 3575 | 456 |
| 5 | 4314 | 456 |
| 6 | 5381 | 456 |
| 0 | 8106 | 447 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
eps |
(-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(cos.f64 x) |
(*.f64 x (*.f64 x eps)) |
x |
(*.f64 x eps) |
eps |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
eps |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
(*.f64 eps eps) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
x |
(*.f64 x #s(literal 4/3 binary64)) |
#s(literal 4/3 binary64) |
#s(literal 1/3 binary64) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
eps |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x x) |
x |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) |
(*.f64 x #s(literal 62/315 binary64)) |
#s(literal 62/315 binary64) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(sin.f64 x) |
(cos.f64 x) |
| Outputs |
|---|
(fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
(fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))))) |
eps |
(-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))) |
(/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1/2 binary64) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(sin.f64 x) |
(tan.f64 x) |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal -1/3 binary64) |
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) |
(/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (cos.f64 x)) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(cos.f64 x) |
(*.f64 x (*.f64 x eps)) |
(*.f64 eps (*.f64 x x)) |
x |
(*.f64 x eps) |
(*.f64 eps x) |
eps |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
eps |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
(*.f64 eps (*.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)))) |
(*.f64 eps eps) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) |
x |
(*.f64 x #s(literal 4/3 binary64)) |
#s(literal 4/3 binary64) |
#s(literal 1/3 binary64) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 x (*.f64 x (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) eps)) eps) |
eps |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(*.f64 x x) |
x |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) |
(*.f64 x #s(literal 62/315 binary64)) |
#s(literal 62/315 binary64) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(tan.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(sin.f64 x) |
(cos.f64 x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (/.f64 (sin.f64 x) (cos.f64 x)) |
| ✓ | accuracy | 99.8% | (tan.f64 (+.f64 x eps)) |
| ✓ | accuracy | 63.7% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
| ✓ | accuracy | 99.8% | (*.f64 x #s(literal 62/315 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
| ✓ | accuracy | 100.0% | (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
| ✓ | accuracy | 99.4% | (*.f64 x #s(literal 4/3 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 x eps) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x eps)) |
| ✓ | accuracy | 100.0% | (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.8% | (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.8% | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
| ✓ | accuracy | 55.7% | (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
| 309.0ms | 240× | 1 | valid |
| 7.0ms | 3× | 3 | valid |
| 6.0ms | 12× | 0 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 511 to 64 computations (87.5% saved)
const: 57.0ms (21.8% of total)ival-mult: 53.0ms (20.3% of total)ival-cos: 46.0ms (17.6% of total)ival-add: 32.0ms (12.2% of total)adjust: 31.0ms (11.8% of total)ival-div: 12.0ms (4.6% of total)ival-pow2: 11.0ms (4.2% of total)ival-tan: 7.0ms (2.7% of total)ival-sin: 7.0ms (2.7% of total)ival-sub: 5.0ms (1.9% of total)exact: 1.0ms (0.4% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))> |
#<alt (fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)> |
#<alt (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))> |
#<alt (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))> |
#<alt (*.f64 x (*.f64 x eps))> |
#<alt (*.f64 x eps)> |
#<alt (fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps)> |
#<alt (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)))> |
#<alt (*.f64 eps eps)> |
#<alt (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))> |
#<alt (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps)> |
#<alt (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))> |
#<alt (*.f64 x x)> |
#<alt (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))> |
#<alt (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))> |
#<alt (tan.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (/.f64 (sin.f64 x) (cos.f64 x))> |
#<alt (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))> |
#<alt (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))> |
#<alt (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))> |
#<alt (*.f64 x #s(literal 4/3 binary64))> |
#<alt (*.f64 x #s(literal 62/315 binary64))> |
#<alt (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))> |
#<alt (cos.f64 x)> |
| Outputs |
|---|
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))> |
#<alt (* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))> |
#<alt (* 1/3 eps)> |
#<alt (+ x (* 1/3 eps))> |
#<alt (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))> |
#<alt (+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<alt (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))> |
#<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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))> |
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (/ (pow (sin x) 2) (pow (cos x) 2))> |
#<alt (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 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)) (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* (pow eps 2) (- (+ 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)) (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))> |
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 1/3> |
#<alt (+ 1/3 (* 4/3 (pow x 2)))> |
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))> |
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps (pow x 2))> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))))> |
#<alt (* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2)))))> |
#<alt (+ eps (* 1/3 (pow eps 3)))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2)))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2)))))> |
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2)))))> |
#<alt (* 4/3 (* (pow eps 3) (pow x 2)))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* 4/3 (* (pow eps 3) (pow x 2)))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2)))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))> |
#<alt (+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2))))> |
#<alt (* 4/3 (* (pow eps 2) (pow x 2)))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (* 4/3 (* (pow eps 2) (pow x 2)))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2))))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt 1/3> |
#<alt (+ 1/3 (* 4/3 (pow x 2)))> |
#<alt (+ 1/3 (* 4/3 (pow x 2)))> |
#<alt (+ 1/3 (* 4/3 (pow x 2)))> |
#<alt (* 4/3 (pow x 2))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* 4/3 (pow x 2))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2)))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))> |
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1)))> |
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1)))> |
#<alt eps> |
#<alt (+ eps (* eps (pow x 2)))> |
#<alt (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))> |
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))> |
#<alt (* 62/315 (* eps (pow x 8)))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2)))))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4))))))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6))))))> |
#<alt (* 62/315 (* eps (pow x 8)))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2)))))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4))))))> |
#<alt (* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6))))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))> |
#<alt (* 62/315 (pow x 8))> |
#<alt (* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<alt (* 62/315 (pow x 8))> |
#<alt (* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt 1> |
#<alt (+ 1 (* 2/3 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))> |
#<alt (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))> |
#<alt (* 62/315 (pow x 6))> |
#<alt (* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<alt (* 62/315 (pow x 6))> |
#<alt (* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<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))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (pow x 4)> |
#<alt (* (pow x 4) (+ 1 (* 1/3 (pow x 2))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2))))))))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (/ (pow (sin x) 4) (pow (cos x) 2))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x)))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 4/3 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt (* 62/315 x)> |
#<alt 2/3> |
#<alt (+ 2/3 (* 17/45 (pow x 2)))> |
#<alt (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))> |
#<alt (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))> |
#<alt (* 62/315 (pow x 4))> |
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* 62/315 (pow x 4))> |
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt (* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 19.0ms | x | @ | inf | (+ (* (+ (* (+ (* eps (- (/ (+ (+ (* (cos (+ x x)) -1/2) 1/2) (pow (* (sin x) (tan x)) 2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (* (+ (pow (tan x) 2) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) |
| 7.0ms | x | @ | 0 | (+ (* eps (* (* eps eps) (+ (* x (* x 4/3)) 1/3))) eps) |
| 6.0ms | eps | @ | -inf | (+ (* eps (- (/ (+ (+ (* (cos (+ x x)) -1/2) 1/2) (pow (* (sin x) (tan x)) 2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (* (+ (pow (tan x) 2) 1) (sin x)) (cos x))) |
| 4.0ms | x | @ | -inf | (+ (* (+ (* (+ (* eps (- (/ (+ (+ (* (cos (+ x x)) -1/2) 1/2) (pow (* (sin x) (tan x)) 2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (* (+ (pow (tan x) 2) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) |
| 4.0ms | x | @ | -inf | (+ (* eps (- (/ (+ (+ (* (cos (+ x x)) -1/2) 1/2) (pow (* (sin x) (tan x)) 2)) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (* (pow (tan x) 2) -1/3) -1/3))) (/ (* (+ (pow (tan x) 2) 1) (sin x)) (cos x))) |
| 1× | batch-egg-rewrite |
| 4 926× | lower-fma.f32 |
| 4 902× | lower-fma.f64 |
| 4 562× | lower-*.f32 |
| 4 542× | lower-*.f64 |
| 3 732× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 50 | 361 |
| 0 | 100 | 346 |
| 1 | 442 | 330 |
| 2 | 3809 | 328 |
| 0 | 9580 | 325 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(*.f64 x (*.f64 x eps)) |
(*.f64 x eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) |
(*.f64 eps eps) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x x) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 4/3 binary64)) |
(*.f64 x #s(literal 62/315 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(cos.f64 x) |
| Outputs |
|---|
(+.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(+.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (neg.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (/.f64 (pow.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64)) (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (neg.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))))))) |
(fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(fma.f64 (sin.f64 x) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (sin.f64 x) (/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(fma.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (tan.f64 x) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (neg.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))))) |
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(*.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/4 binary64))))) |
(*.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))))) #s(literal -1/4 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (pow.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))))) |
(*.f64 x #s(literal 4/3 binary64)) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 x #s(literal 62/315 binary64)) |
(*.f64 #s(literal 62/315 binary64) x) |
(+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) |
(+.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal 2/3 binary64)) |
(+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(+.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))) |
(-.f64 (/.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64))) (/.f64 #s(literal 4/9 binary64) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)))) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) |
(fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 62/315 binary64))) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 x (*.f64 (*.f64 x #s(literal 62/315 binary64)) (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 x #s(literal 62/315 binary64)) (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal 62/315 binary64)) (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 62/315 binary64)) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) x #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 62/315 binary64) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 62/315 binary64)) x) x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x #s(literal 62/315 binary64))) x (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))) (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64)))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64)) (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64))))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64)) (+.f64 #s(literal 4/9 binary64) (-.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))))) |
(/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64)) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))) (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64))) (neg.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64))) (neg.f64 (+.f64 #s(literal 4/9 binary64) (-.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64))))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64))) (neg.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)))) |
(/.f64 (-.f64 #s(literal 4/9 binary64) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))))) (-.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 4/9 binary64) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))))) (neg.f64 (-.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))))) |
(pow.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))) (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)) (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))))) #s(literal 8/27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))))) #s(literal 4/9 binary64)) (*.f64 x (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)))) #s(literal -4/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal -2/3 binary64)))) |
(cos.f64 x) |
| 1× | egg-herbie |
| 9 262× | lower-fma.f64 |
| 9 262× | lower-fma.f32 |
| 7 386× | lower-*.f64 |
| 7 386× | lower-*.f32 |
| 2 906× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 520 | 9554 |
| 1 | 1658 | 9453 |
| 2 | 5247 | 9146 |
| 0 | 8797 | 8553 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* 1/3 eps) |
(+ x (* 1/3 eps)) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
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(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(* 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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps))))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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))))) |
(/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 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)) (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* (pow eps 2) (- (+ 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)) (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* eps x)) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))) |
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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))) |
1/3 |
(+ 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 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps (pow x 2)) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
eps |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ 1 (pow eps 2))))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (/ 1 (pow eps 2))))) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* 4/3 (* (pow eps 3) (pow x 2))))) |
(* 4/3 (* (pow eps 3) (pow x 2))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* 4/3 (* (pow eps 3) (pow x 2))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* 4/3 (pow eps 3)) (/ eps (pow x 2))))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* 1/3 (pow eps 2)) |
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2)))) |
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2)))) |
(+ (* 1/3 (pow eps 2)) (* 4/3 (* (pow eps 2) (pow x 2)))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (* 4/3 (pow eps 2)))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* 4/3 (pow x 2))) |
(* 4/3 (pow x 2)) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* 4/3 (pow x 2)) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps)))))) |
(* 62/315 (* eps (pow x 8))) |
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2))))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4)))))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6)))))) |
(* 62/315 (* eps (pow x 8))) |
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2))))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4)))))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6)))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(* 62/315 (pow x 8)) |
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* 62/315 (pow x 8)) |
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
1 |
(+ 1 (* 2/3 (pow x 2))) |
(+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) |
(+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))) |
(* 62/315 (pow x 6)) |
(* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* 62/315 (pow x 6)) |
(* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(/ (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)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 4/3 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
(* 62/315 x) |
2/3 |
(+ 2/3 (* 17/45 (pow x 2))) |
(+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))) |
(+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))) |
(* 62/315 (pow x 4)) |
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* 62/315 (pow x 4)) |
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
| Outputs |
|---|
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) |
(/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) #s(literal 1/3 binary64))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) #s(literal 1/3 binary64))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) #s(literal 1/3 binary64))))) |
(* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (fma.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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (fma.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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps))))) |
(* -1 (* eps (+ (* -1 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
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(* 1/3 eps) |
(*.f64 eps #s(literal 1/3 binary64)) |
(+ x (* 1/3 eps)) |
(fma.f64 eps #s(literal 1/3 binary64) x) |
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x))))) |
(fma.f64 x (fma.f64 x (*.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) |
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x)))))) |
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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 (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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 (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) |
(fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (*.f64 eps (*.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* (pow eps 3) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1/2 (/ (cos (neg (* -2 x))) (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))))) (* -1/3 (/ (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))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (*.f64 eps eps) (fma.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 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) #s(literal 1/3 binary64))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (*.f64 eps (fma.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 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))) |
(* (pow eps 2) (- (+ 1/3 (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)))) (fma.f64 (/.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) (+.f64 (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64) #s(literal 1/3 binary64)))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ 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)) (+ (* -1/2 (/ (cos (* 2 x)) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/ (pow (sin x) 4) (* (pow (cos x) 2) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* 4/3 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 4/3 binary64))) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(* (pow x 2) (+ 4/3 (* 1/3 (/ 1 (pow x 2))))) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
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(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
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(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))))) |
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(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
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(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
(* -1 (* eps (- (* -1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))) 1))) |
(fma.f64 (*.f64 eps (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) eps) |
eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 x (*.f64 x eps) eps) |
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps)))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 eps #s(literal 2/3 binary64) (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 17/45 binary64))) eps) eps) |
(* 62/315 (* eps (pow x 8))) |
(*.f64 eps (*.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 8 binary64)))) |
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 17/45 binary64) (*.f64 eps #s(literal 62/315 binary64)))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4)))))) |
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(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6)))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (fma.f64 eps #s(literal 62/315 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 17/45 binary64) (fma.f64 eps (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 eps (pow.f64 x #s(literal 6 binary64))))))) |
(* 62/315 (* eps (pow x 8))) |
(*.f64 eps (*.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 8 binary64)))) |
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 17/45 binary64) (*.f64 eps #s(literal 62/315 binary64)))) |
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4)))))) |
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(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6)))))) |
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(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
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(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
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(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
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(* 62/315 (pow x 8)) |
(*.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 8 binary64))) |
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 17/45 binary64) (*.f64 x x)))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
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(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
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(* 62/315 (pow x 8)) |
(*.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 8 binary64))) |
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 17/45 binary64) (*.f64 x x)))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 2/3 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(* 62/315 (pow x 6)) |
(*.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 6 binary64))) |
(* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 17/45 binary64) (*.f64 x x)))) |
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(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
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(* 62/315 (pow x 6)) |
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(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(fma.f64 #s(literal 62/315 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) #s(literal 1 binary64))) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(* 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 |
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(+.f64 x eps) |
(+ eps x) |
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(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
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(fma.f64 x (/.f64 eps x) x) |
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(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(+ eps x) |
(+.f64 x eps) |
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eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
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(fma.f64 eps (/.f64 x eps) eps) |
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(fma.f64 eps (/.f64 x eps) eps) |
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(fma.f64 eps (/.f64 x eps) eps) |
x |
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 5/3 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 77/45 binary64) #s(literal 5/3 binary64))) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 88/63 binary64) #s(literal 77/45 binary64))) #s(literal 5/3 binary64)) #s(literal 1 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (* 2 x))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(/ (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (/ (pow (sin x) 4) (pow (cos x) 2)))) (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 4/3 x) |
(*.f64 x #s(literal 4/3 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
(* 62/315 x) |
(*.f64 x #s(literal 62/315 binary64)) |
2/3 |
#s(literal 2/3 binary64) |
(+ 2/3 (* 17/45 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(* 62/315 (pow x 4)) |
(*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))) |
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 17/45 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* 62/315 (pow x 4)) |
(*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))) |
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 17/45 binary64) (*.f64 x x)))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* (pow x 4) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) |
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 (/.f64 #s(literal 17/45 binary64) (*.f64 x x)) (+.f64 #s(literal 62/315 binary64) (/.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
Compiled 46 764 to 2 987 computations (93.6% saved)
34 alts after pruning (28 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 053 | 9 | 1 062 |
| Fresh | 5 | 19 | 24 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 060 | 34 | 1 094 |
| Status | Accuracy | Program |
|---|---|---|
| 98.6% | (fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.2% | (fma.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.6% | (fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 98.2% | (fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| 97.5% | (fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) | |
| 96.9% | (fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) | |
| 98.1% | (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) | |
| 97.6% | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) | |
| 96.8% | (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) | |
| 97.4% | (fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| 97.4% | (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) | |
| 97.7% | (fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) | |
| 97.7% | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) | |
| 97.7% | (fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) | |
| ✓ | 96.8% | (fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
| 96.8% | (fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) | |
| 97.4% | (fma.f64 eps (*.f64 x (+.f64 x eps)) eps) | |
| 97.7% | (fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) | |
| ✓ | 97.4% | (fma.f64 eps (*.f64 x x) eps) |
| 63.7% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 36.1% | (-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) | |
| 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) | |
| ✓ | 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
| 63.5% | (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) | |
| 51.0% | (-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) | |
| 29.1% | (-.f64 (tan.f64 (+.f64 x eps)) (pow.f64 (sqrt.f64 (tan.f64 x)) #s(literal 2 binary64))) | |
| ✓ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | 63.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 97.8% | (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) | |
| 97.4% | (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) | |
| 98.1% | (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) | |
| 6.5% | (*.f64 (*.f64 x x) eps) | |
| ✓ | 6.5% | (*.f64 x (*.f64 x eps)) |
| 5.8% | (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
Compiled 1 892 to 647 computations (65.8% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(-.f64 (tan.f64 (fma.f64 eps (/.f64 x eps) eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(fma.f64 (fma.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (tan.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (pow.f64 (sqrt.f64 (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(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)) (neg.f64 (tan.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(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 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
| Outputs |
|---|
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
3 calls:
| 18.0ms | eps |
| 17.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 16.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | eps |
| 98.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(-.f64 (tan.f64 (fma.f64 eps (/.f64 x eps) eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(fma.f64 (fma.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (tan.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (pow.f64 (sqrt.f64 (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(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)) (neg.f64 (tan.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(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 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
| Outputs |
|---|
(fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
3 calls:
| 30.0ms | eps |
| 15.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 15.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | eps |
| 98.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(-.f64 (tan.f64 (fma.f64 eps (/.f64 x eps) eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(fma.f64 (fma.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (tan.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (pow.f64 (sqrt.f64 (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(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)) (neg.f64 (tan.f64 x))) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (fma.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)) (*.f64 (*.f64 eps eps) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
| Outputs |
|---|
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
3 calls:
| 35.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 14.0ms | x |
| 14.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | eps |
| 98.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(-.f64 (tan.f64 (fma.f64 eps (/.f64 x eps) eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x)) |
(fma.f64 (fma.f64 eps (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) x) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (tan.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (pow.f64 (sqrt.f64 (tan.f64 x)) #s(literal 2 binary64))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(-.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (fma.f64 x x (*.f64 (neg.f64 eps) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps)))))) (tan.f64 x)) |
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(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)) (neg.f64 (tan.f64 x))) |
| Outputs |
|---|
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
3 calls:
| 49.0ms | eps |
| 14.0ms | x |
| 13.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 98.2% | 1 | x |
| 98.2% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
| Outputs |
|---|
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
3 calls:
| 38.0ms | eps |
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | eps |
| 98.1% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (/.f64 (*.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))) #s(literal 1 binary64))) eps) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 x (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (*.f64 x (*.f64 x x)) x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
3 calls:
| 23.0ms | x |
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.8% | 1 | x |
| 97.8% | 1 | eps |
| 97.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 7/45 binary64) #s(literal 1/3 binary64)) #s(literal 2/3 binary64))) #s(literal 1 binary64))) eps) |
| Outputs |
|---|
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
3 calls:
| 16.0ms | x |
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.8% | 1 | x |
| 97.8% | 1 | eps |
| 97.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
| Outputs |
|---|
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
3 calls:
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
| 97.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
| Outputs |
|---|
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
3 calls:
| 25.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
| 97.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (*.f64 x x)) eps) |
| Outputs |
|---|
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
3 calls:
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (*.f64 x (*.f64 x #s(literal 4/3 binary64)))) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64))) eps) |
| Outputs |
|---|
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
3 calls:
| 25.0ms | eps |
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | x |
| 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 |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 x x))) |
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) eps) |
(fma.f64 eps (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps eps) |
| Outputs |
|---|
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
3 calls:
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | eps |
| 3.0ms | x |
| 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 |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
| Outputs |
|---|
(fma.f64 eps (*.f64 x x) eps) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| 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 |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
| Outputs |
|---|
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
3 calls:
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 97.4% | 1 | x |
Compiled 15 to 10 computations (33.3% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(*.f64 x (*.f64 x eps)) |
(*.f64 (*.f64 x x) eps) |
| Outputs |
|---|
(*.f64 x (*.f64 x eps)) |
3 calls:
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | x |
| 1.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 6.5% | 1 | eps |
| 6.5% | 1 | x |
| 6.5% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 36× | *-commutative_binary64 |
| 12× | +-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 250 |
| 1 | 108 | 250 |
| 2 | 112 | 250 |
| 3 | 114 | 250 |
| 4 | 115 | 250 |
| 1× | saturated |
| Inputs |
|---|
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(*.f64 x (*.f64 x eps)) |
| Outputs |
|---|
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 (fma.f64 eps #s(literal 1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (fma.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) |
(fma.f64 eps (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps) |
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) eps) |
(*.f64 eps (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 62/315 binary64)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 eps (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps) |
(fma.f64 eps (fma.f64 x (+.f64 x eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
(fma.f64 eps (*.f64 x (+.f64 x eps)) eps) |
(fma.f64 eps (*.f64 x x) eps) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(*.f64 eps (fma.f64 x x #s(literal 1 binary64))) |
(*.f64 x (*.f64 x eps)) |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 9 262× | lower-fma.f64 |
| 9 262× | lower-fma.f32 |
| 8 808× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 664 | 8261 |
| 1 | 2174 | 8028 |
| 2 | 6814 | 7832 |
| 0 | 8326 | 7329 |
| 0 | 52 | 356 |
| 0 | 106 | 354 |
| 1 | 482 | 278 |
| 2 | 4172 | 265 |
| 0 | 8533 | 262 |
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 0 | 50 | 361 |
| 0 | 100 | 346 |
| 1 | 442 | 330 |
| 2 | 3809 | 328 |
| 0 | 9580 | 325 |
| 0 | 594 | 8175 |
| 1 | 1794 | 7938 |
| 2 | 5636 | 7788 |
| 0 | 8437 | 7427 |
| 0 | 520 | 9554 |
| 1 | 1658 | 9453 |
| 2 | 5247 | 9146 |
| 0 | 8797 | 8553 |
| 0 | 45 | 331 |
| 0 | 88 | 309 |
| 1 | 418 | 217 |
| 2 | 3681 | 213 |
| 0 | 8180 | 205 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 690 to 334 computations (51.6% saved)
Compiled 604 to 224 computations (62.9% saved)
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