
Time bar (total: 16.0s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.6s | 25 804× | 0 | invalid |
| 1.0s | 2 819× | 1 | valid |
| 620.0ms | 5 437× | 0 | valid |
ival-tan: 936.0ms (25.3% of total)const: 872.0ms (23.6% of total)ival-<=: 487.0ms (13.2% of total)ival-mult: 315.0ms (8.5% of total)ival-add: 254.0ms (6.9% of total)ival-fabs: 228.0ms (6.2% of total)ival-sub: 199.0ms (5.4% of total)ival-<: 172.0ms (4.6% of total)ival-and: 101.0ms (2.7% of total)adjust: 81.0ms (2.2% of total)exact: 42.0ms (1.1% of total)ival-assert: 13.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 219 | 2 | (-1.8662976358927449e-93 9.753130905532037e-96) | 0 | - | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4 | 0 | - | 1 | (-27.13751048393653 0.00830535423938035) | (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 | 221 | 5 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 3 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 222 | 1 |
| - | 2 | 31 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 222 | 1 | 0 |
| - | 2 | 4 | 27 |
| number | freq |
|---|---|
| 0 | 32 |
| 1 | 224 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 23.0ms | 194× | 1 | valid |
| 16.0ms | 316× | 0 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 49 to 22 computations (55.1% saved)
ival-tan: 14.0ms (56.3% of total)adjust: 4.0ms (16.1% of total)ival-add: 3.0ms (12.1% of total)ival-sub: 3.0ms (12.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
| 102× | sub-neg |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 68× | cancel-sign-sub-inv |
| 64× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 6 computations (33.3% saved)
Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 59.9% | (-.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 | 0 | (+.f64 x eps) | |
| accuracy | 0 | (tan.f64 x) | |
| accuracy | 0.16142705824541267 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 25.483648671101708 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | 97× | 1 | valid |
| 8.0ms | 158× | 0 | valid |
| 0.0ms | 1× | 3 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 5.0ms (49.7% of total)adjust: 2.0ms (19.9% of total)ival-add: 2.0ms (19.9% of total)ival-sub: 1.0ms (9.9% 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 | x | @ | inf | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | 0 | (- (tan (+ x eps)) (tan x)) |
| 1.0ms | x | @ | -inf | (- (tan (+ x eps)) (tan 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 (+.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 #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)) (/.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 (+.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 #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)) (/.f64 (sin.f64 x) (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))) (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))) (/.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 (+.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 #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)) (/.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 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))) |
(* 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)) |
| 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))) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 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 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 #s(literal 1 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))))) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 (tan.f64 (+.f64 x eps)) (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 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 (+.f64 x eps))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 x eps)))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (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 #s(literal -1 binary64) (tan.f64 x) (tan.f64 (+.f64 x eps))) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3/2 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 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (-.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 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 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (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 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #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))))) |
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (sin.f64 (+.f64 (+.f64 x eps) x))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.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)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(fma.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 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 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(neg.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (neg.f64 (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 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) |
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (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))))) |
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (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 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (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 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
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(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (/.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))) |
(*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))) #s(literal -1 binary64))) |
(+.f64 x eps) |
(+.f64 eps x) |
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps)))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(neg.f64 (/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x)))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) |
(/.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 (-.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 x eps) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (*.f64 eps eps)) (-.f64 x eps))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (-.f64 x eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (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)) |
Compiled 8 701 to 985 computations (88.7% saved)
21 alts after pruning (20 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 316 | 20 | 336 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 316 | 21 | 337 |
| Status | Accuracy | Program |
|---|---|---|
| 60.1% | (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| 60.1% | (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))) | |
| ▶ | 59.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
| 59.1% | (/.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)))) | |
| 58.9% | (/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| ▶ | 31.1% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| 59.9% | (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) | |
| 59.9% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) | |
| 59.9% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 60.1% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ▶ | 59.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
| 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 58.3% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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))) | |
| ▶ | 58.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
| 58.2% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) | |
| 58.1% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan 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)) | |
| ▶ | 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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)) |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
Compiled 923 to 476 computations (48.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) | |
| cost-diff | 320 | (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 704 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 16128 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) | |
| cost-diff | 320 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) | |
| cost-diff | 0 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) | |
| cost-diff | 1408 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) | |
| cost-diff | 0 | #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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 | 192 | (+.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 #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)) | |
| cost-diff | 5824 | (fma.f64 eps (fma.f64 eps (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 #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)) (/.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))) |
| 17 994× | lower-fma.f32 |
| 17 980× | lower-fma.f64 |
| 4 548× | lower-*.f32 |
| 4 538× | lower-*.f64 |
| 2 690× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 749 |
| 0 | 106 | 711 |
| 1 | 203 | 629 |
| 2 | 468 | 626 |
| 3 | 1307 | 626 |
| 4 | 4830 | 626 |
| 0 | 8072 | 616 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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 eps (fma.f64 eps (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 #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)) (/.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 (+.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 #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)) (/.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 (+.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 #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)) (/.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))) (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)) |
(-.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 #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) |
(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) |
(/.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) |
#s(literal -1/6 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)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 x x) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.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 (*.f64 eps 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))) eps))) |
(fma.f64 eps (fma.f64 eps (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 #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)) (/.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 (/.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 (*.f64 eps 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))) eps)) |
eps |
(fma.f64 eps (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 #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)) (/.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 (+.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 #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)) (/.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 (+.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 #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)) |
(+.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 (+.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 #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 1/2 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) |
(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)) |
#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 -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(literal -1/6 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)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x) |
(*.f64 x x) |
(*.f64 x #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(tan.f64 (+.f64 x eps)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal 1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.1614270582454127 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.2421875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) | |
| accuracy | 25.831941943357254 | (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) | |
| accuracy | 32.88308728276191 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| accuracy | 0.01953125 | (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) | |
| accuracy | 0.11960381926531669 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 0.1445461029410982 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 25.507789669205355 | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.1614270582454127 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.2421875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) | |
| accuracy | 0.28125 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) | |
| accuracy | 25.483648671101708 | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) | |
| accuracy | 0.1614270582454127 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.37109375 | (*.f64 x #s(literal 1/3 binary64)) | |
| accuracy | 1.4057583736303774 | #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) | |
| accuracy | 25.483648671101708 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) | |
| accuracy | 0.03810502930532605 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.12109375 | (fma.f64 eps (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 #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)) (/.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 | 0.8767330748578341 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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)) | |
| accuracy | 0.982753759768442 | (+.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 #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)) |
| 116.0ms | 102× | 1 | valid |
| 67.0ms | 151× | 0 | valid |
| 8.0ms | 3× | 3 | valid |
Compiled 677 to 60 computations (91.1% saved)
ival-add: 37.0ms (23.6% of total)ival-mult: 29.0ms (18.5% of total)ival-div: 24.0ms (15.3% of total)adjust: 13.0ms (8.3% of total)const: 10.0ms (6.4% of total)ival-pow: 10.0ms (6.4% of total)ival-tan: 7.0ms (4.5% of total)ival-pow2: 7.0ms (4.5% of total)ival-sub: 6.0ms (3.8% of total)ival-cos: 6.0ms (3.8% of total)ival-sin: 5.0ms (3.2% of total)ival-neg: 1.0ms (0.6% of total)exact: 1.0ms (0.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (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 (+.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 #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)) (/.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 (-.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 #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))> |
#<alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)))> |
#<alt (tan.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))> |
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))))> |
#<alt (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x))> |
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))> |
#<alt (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))> |
#<alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))> |
#<alt (cos.f64 (+.f64 x eps))> |
#<alt (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))> |
#<alt (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))> |
#<alt (fma.f64 eps (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 #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)) (/.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 (pow.f64 (sin.f64 x) #s(literal 4 binary64))> |
#<alt (*.f64 x #s(literal 1/3 binary64))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)))> |
| 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 (* 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 (+ (/ (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 (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 (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 (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 (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 (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 (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 (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 (/ (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 (+ (/ (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)))> |
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#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos eps) (sin eps))> |
#<alt (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))> |
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos x) (sin x))> |
#<alt (+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))> |
#<alt (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))> |
#<alt (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<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 (pow x 4)> |
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#<alt (pow (sin x) 4)> |
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#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
#<alt (* 1/3 x)> |
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#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
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#<alt (sin (- eps (* -1 x)))> |
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#<alt (sin (- eps (* -1 x)))> |
#<alt (sin x)> |
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#<alt (/ 1 x)> |
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#<alt (/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x)> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
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#<alt (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))))> |
#<alt (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
120 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | x | @ | inf | (* (/ 1 (tan (+ x eps))) (/ 1 (tan x))) |
| 7.0ms | x | @ | inf | (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 5.0ms | x | @ | 0 | (/ 1 (tan (+ x eps))) |
| 4.0ms | eps | @ | 0 | (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) |
| 4.0ms | x | @ | -inf | (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) |
| 1× | egg-herbie |
| 9 474× | lower-fma.f64 |
| 9 474× | lower-fma.f32 |
| 7 394× | lower-*.f64 |
| 7 394× | lower-*.f32 |
| 5 076× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 746 | 14389 |
| 1 | 2391 | 13723 |
| 0 | 8282 | 13377 |
| 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 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
(- (+ 1/3 (+ (/ (pow (sin x) 2) (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 (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 (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 (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 (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 (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 (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 (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 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)) |
(+ (/ (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)))) |
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x |
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x |
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(/ (cos x) (sin x)) |
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(/ (cos eps) (* x (sin eps))) |
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(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x)))) |
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(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x))))) |
(/ (pow (cos x) 2) (pow (sin x) 2)) |
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(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
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(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
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(/ (cos eps) (sin eps)) |
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(/ (cos (+ eps x)) (sin (+ eps x))) |
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(/ (cos x) (sin x)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (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 (- x (* -1 eps)))) |
(/ (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))) |
(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) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(* 1/3 x) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(/ 1 x) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
| 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 (*.f64 x 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 (*.f64 x 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 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 (/.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 -1/2 binary64)) |
(* 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) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* 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))))) |
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(* 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))))) |
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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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(* (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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1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 4/3 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
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(/ (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 x (/.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))) |
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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 (- (+ 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)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
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(/ (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))) |
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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 |
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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) |
(* -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))) |
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(fma.f64 (neg.f64 eps) (/.f64 x (neg.f64 eps)) eps) |
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(fma.f64 x (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(- (/ (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))) |
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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))) |
(* 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 (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(- (/ (sin (+ 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))) |
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(-.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))) |
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(-.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))) |
(/ (cos eps) (sin eps)) |
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(/ 1 (cos eps)) |
(/.f64 #s(literal 1 binary64) (cos.f64 eps)) |
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(* 1/3 (pow eps 2)) |
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(pow (sin x) 4) |
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(*.f64 eps (fma.f64 eps (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x)))) (sin.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x)))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(*.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (-.f64 (fma.f64 eps (+.f64 (neg.f64 (fma.f64 (cos.f64 x) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (-.f64 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x)))) (sin.f64 x)))) (sin.f64 x)) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x))) (+.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))))) (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))) (/.f64 (*.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x)))) (sin.f64 x))) (/.f64 (*.f64 (cos.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 x))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.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)) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
| 5 126× | lower-fma.f32 |
| 5 112× | lower-fma.f64 |
| 4 510× | lower-*.f32 |
| 4 500× | lower-*.f64 |
| 3 496× | lower-pow.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 462 |
| 0 | 106 | 417 |
| 1 | 488 | 311 |
| 2 | 4317 | 303 |
| 0 | 9260 | 293 |
| 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 (+.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 #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)) (/.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 (-.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 #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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(fma.f64 eps (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 #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)) (/.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)))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(*.f64 x #s(literal 1/3 binary64)) |
(sin.f64 (+.f64 x eps)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
| 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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 binary64)))) |
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 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 (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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #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))))))) |
(/.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 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 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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)))))) |
(/.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))))) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 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 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) |
(/.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 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 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)))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 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)))) (neg.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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 binary64))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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)))) (neg.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 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal -1/8 binary64)) (+.f64 (pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))))) |
(/.f64 (-.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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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 (pow.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))) |
(pow.f64 (/.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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/216 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)))) #s(literal -1 binary64)) |
(pow.f64 (/.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 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/36 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)))) #s(literal -1 binary64)) |
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (neg.f64 (tan.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) (*.f64 (tan.f64 x) (neg.f64 (tan.f64 (+.f64 x eps))))) |
(/.f64 (-.f64 (neg.f64 (tan.f64 (+.f64 x eps))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (neg.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(/.f64 (-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 x eps))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -3 binary64)))) (neg.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -3 binary64)))) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))))) |
(pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -3 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -2 binary64)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))) |
Compiled 63 384 to 3 521 computations (94.4% saved)
33 alts after pruning (29 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 713 | 20 | 1 733 |
| Fresh | 6 | 9 | 15 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 721 | 33 | 1 754 |
| Status | Accuracy | Program |
|---|---|---|
| 60.1% | (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))) | |
| 59.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) | |
| ✓ | 59.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
| 32.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) | |
| 58.7% | (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| 59.1% | (/.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)))) | |
| 58.9% | (/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 27.2% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| ▶ | 30.1% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
| 29.5% | (/.f64 (-.f64 #s(approx (* 1 (/ 1 (tan x))) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 59.9% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 60.1% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 59.8% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 59.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
| ▶ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 58.3% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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))) | |
| ✓ | 58.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
| 58.1% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) | |
| ▶ | 98.0% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
| ▶ | 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (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)) |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan 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)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 248/135 binary64)) #s(literal 17/9 binary64))) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 x (*.f64 x #s(literal 4/3 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)))) eps)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) | |
| 97.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) | |
| 97.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) | |
| ▶ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
Compiled 1 662 to 856 computations (48.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 320 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) | |
| cost-diff | 320 | (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 12224 | (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) | |
| cost-diff | 16128 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) | |
| 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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 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 | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) | |
| cost-diff | 0 | #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) | |
| cost-diff | 0 | (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) 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))) |
| 13 918× | lower-fma.f32 |
| 13 904× | lower-fma.f64 |
| 5 120× | lower-*.f32 |
| 5 104× | lower-*.f64 |
| 2 192× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 92 | 870 |
| 0 | 151 | 834 |
| 1 | 277 | 791 |
| 2 | 613 | 777 |
| 3 | 1655 | 765 |
| 4 | 6470 | 765 |
| 0 | 8162 | 733 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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 (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) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
eps |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
(-.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) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.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) |
eps |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) |
(*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)) |
(log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(literal -1 binary64) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.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 (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 (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 (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 (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 eps (/.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 (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 eps (/.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 (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 (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) (*.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 (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) (*.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 (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) (*.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) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
eps |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
(-.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) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan 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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps 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) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
eps |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)) |
(neg.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))) |
(log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(log.f64 (*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) |
(*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) |
#s(literal -1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 2.400402403788072 | (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) | |
| accuracy | 25.831941943357254 | (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) | |
| accuracy | 32.87918103276191 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) | |
| accuracy | 33.02661798939174 | (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.0078125 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.01953125 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.7723290724032159 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.00390625 | (/.f64 (sin.f64 x) (cos.f64 x)) | |
| accuracy | 0.05044535675211428 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 25.475836171101708 | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| accuracy | 0 | (*.f64 eps eps) | |
| accuracy | 0.18359375 | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) | |
| accuracy | 0.38438388007651525 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) | |
| accuracy | 25.95937496323176 | #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) | |
| accuracy | 0.11947250976844202 | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) | |
| accuracy | 0.12109375 | (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 | 0.38438388007651525 | #s(approx (- (tan (+ x eps)) (tan x)) (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)) | |
| accuracy | 25.85402215918345 | (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) |
| 356.0ms | 243× | 1 | valid |
| 7.0ms | 2× | 3 | valid |
| 6.0ms | 9× | 0 | valid |
| 1.0ms | 2× | 0 | invalid |
Compiled 721 to 84 computations (88.3% saved)
ival-mult: 59.0ms (18.5% of total)ival-cos: 50.0ms (15.7% of total)adjust: 46.0ms (14.5% of total)ival-div: 39.0ms (12.3% of total)ival-add: 36.0ms (11.3% of total)ival-pow2: 17.0ms (5.3% of total)const: 17.0ms (5.3% of total)ival-pow: 14.0ms (4.4% of total)ival-sub: 12.0ms (3.8% of total)ival-log: 10.0ms (3.1% of total)ival-tan: 7.0ms (2.2% of total)ival-exp: 6.0ms (1.9% of total)ival-sin: 3.0ms (0.9% of total)exact: 1.0ms (0.3% 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 #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps))> |
#<alt (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)> |
#<alt #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))> |
#<alt (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))> |
#<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 #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))> |
#<alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps 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 (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))))> |
#<alt (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))> |
#<alt (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))> |
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))> |
#<alt #s(approx (- (tan (+ x eps)) (tan x)) (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))> |
#<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 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))> |
#<alt (*.f64 eps eps)> |
#<alt (cos.f64 x)> |
#<alt (pow.f64 (cos.f64 x) #s(literal 2 binary64))> |
#<alt (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))> |
#<alt (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)))> |
| 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 (/ (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 (* 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 (/ (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))))))))> |
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#<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)))> |
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#<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 (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
#<alt (* 1/3 (pow eps 2))> |
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#<alt (* 1/3 (pow eps 2))> |
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#<alt (* 1/3 (pow eps 2))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
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#<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)))> |
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#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))> |
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#<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)))))> |
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#<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)))> |
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#<alt (/ (sin eps) (cos eps))> |
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#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
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#<alt (/ (sin (+ eps x)) (cos (+ eps x)))> |
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#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))> |
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#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))> |
#<alt eps> |
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#<alt (+ eps x)> |
#<alt x> |
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#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt eps> |
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#<alt (* eps (+ 1 (/ x eps)))> |
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#<alt (/ (sin x) (cos x))> |
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#<alt (/ (sin x) (cos x))> |
#<alt (/ (sin x) (cos x))> |
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#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
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#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
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#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<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 (* 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 (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)> |
#<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 (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 (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
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#<alt (* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
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#<alt (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
#<alt (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))))> |
132 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 59.0ms | x | @ | -inf | (log (* (tan (+ x eps)) (tan x))) |
| 45.0ms | x | @ | inf | (log (* (tan (+ x eps)) (tan x))) |
| 22.0ms | eps | @ | -inf | (log (* (tan (+ x eps)) (tan x))) |
| 19.0ms | eps | @ | inf | (log (* (tan (+ x eps)) (tan x))) |
| 10.0ms | eps | @ | 0 | (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) |
| 1× | egg-herbie |
| 9 410× | lower-fma.f64 |
| 9 410× | lower-fma.f32 |
| 7 042× | lower-*.f64 |
| 7 042× | lower-*.f32 |
| 6 242× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 855 | 18952 |
| 1 | 2820 | 18177 |
| 0 | 8817 | 17593 |
| 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))))) |
(/ (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))) |
(* 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))))) |
(/ (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))) |
(* 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)) |
(/ (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)) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
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))) |
(* 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))) |
(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) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* 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))) |
(/ (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 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 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 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
1 |
(+ 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) |
(+ (log x) (log (/ (sin eps) (cos eps)))) |
(+ (log x) (+ (log (/ (sin eps) (cos eps))) (/ (* x (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps)))) |
(+ (log x) (+ (log (/ (sin eps) (cos eps))) (* x (+ (* 1/2 (* x (+ (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))) (* 2 (/ (* (cos eps) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (sin eps)))))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))))) |
(+ (log x) (+ (log (/ (sin eps) (cos eps))) (* x (+ (* x (+ (* 1/6 (* x (+ (* -6 (/ (* (pow (cos eps) 2) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (+ (* 2 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 3)) (pow (sin eps) 3))) (* 6 (/ (* (cos eps) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (sin eps))))))) (* 1/2 (+ (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))) (* 2 (/ (* (cos eps) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (sin eps))))))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (- eps (* -1 x)))) (* (cos x) (cos (- eps (* -1 x)))))) |
(log (/ (* (sin x) (sin (- eps (* -1 x)))) (* (cos x) (cos (- eps (* -1 x)))))) |
(log (/ (* (sin x) (sin (- eps (* -1 x)))) (* (cos x) (cos (- eps (* -1 x)))))) |
(log (/ (* (sin x) (sin (- eps (* -1 x)))) (* (cos x) (cos (- eps (* -1 x)))))) |
(log (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ (log (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) |
(+ (log (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* 1/2 (* eps (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* 2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) |
(+ (log (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* eps (+ (* 1/6 (* eps (+ (* -6 (/ (* (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))))))) (sin x))) (+ (* -6 (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x))) (* 2 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 3)) (pow (sin x) 3))))))) (* 1/2 (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* 2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (+ eps x))) (* (cos x) (cos (+ eps x))))) |
(log (/ (* (sin x) (sin (- x (* -1 eps)))) (* (cos x) (cos (- x (* -1 eps)))))) |
(log (/ (* (sin x) (sin (- x (* -1 eps)))) (* (cos x) (cos (- x (* -1 eps)))))) |
(log (/ (* (sin x) (sin (- x (* -1 eps)))) (* (cos x) (cos (- x (* -1 eps)))))) |
(log (/ (* (sin x) (sin (- x (* -1 eps)))) (* (cos x) (cos (- x (* -1 eps)))))) |
(/ 1 x) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
| Outputs |
|---|
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(+ (* eps (- (+ 1/3 (+ (* 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 (/.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 (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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (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 (/.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 (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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (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 (/.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 (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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (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))))))))) |
(*.f64 eps (+.f64 #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 (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))))))) |
(* 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))))))))) |
(*.f64 eps (+.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (+.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 (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 #s(literal 1/3 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))))))) |
(* 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))))))))) |
(*.f64 eps (+.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (+.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 (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 #s(literal 1/3 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))))))) |
(* 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))))))))) |
(*.f64 eps (+.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps))) (+.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 (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 #s(literal 1/3 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))))))) |
(* 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))))))))) |
(*.f64 eps (+.f64 #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 (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))))))) |
(* -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))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.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 (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 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)))) |
(* -1 (* eps (+ (* -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))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.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 (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 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)))) |
(* -1 (* eps (+ (* -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))))) |
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.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 (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 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)))) |
(* 1/3 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 #s(literal 4/3 binary64) (*.f64 x eps) #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 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64))) |
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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 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 61/120 binary64) #s(literal 5/6 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2)))))))) |
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(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 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))) |
(* (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)))) |
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(- 1/2 (* 1/2 (cos (* 2 x)))) |
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(- 1/2 (* 1/2 (cos (* 2 x)))) |
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(- 1/2 (* 1/2 (cos (* 2 x)))) |
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(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
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(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
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(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
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(- 1/2 (* 1/2 (cos (neg (* -2 x))))) |
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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 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
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(+ 1/2 (* 1/2 (cos (* 2 x)))) |
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(+ 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)) |
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(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))))) |
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(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 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 (- 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 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))))) |
(+.f64 eps (*.f64 eps (+.f64 (/.f64 (*.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (neg.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))) (neg.f64 eps) #s(literal -1/6 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 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))) |
(* eps (+ 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) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 eps (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.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 (fma.f64 eps (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (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 (fma.f64 eps (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (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)))))) |
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (*.f64 eps eps))) |
(* (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) #s(literal 1/3 binary64))) (*.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)))))) |
(* (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))) (*.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)))))) |
(* (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)))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))) (*.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)))))) |
(* (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)))))) |
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (*.f64 eps 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 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))))) |
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(* 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))))) |
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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))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
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(/ (sin (+ eps x)) (cos (+ eps x))) |
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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 (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
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(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
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(/ (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))) |
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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))))) (/ (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))) |
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
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(/.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))) |
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) |
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 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
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(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 eps (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
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(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x) |
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(/.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) |
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(pow (sin x) 2) |
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(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(pow (sin x) 2) |
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(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)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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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))))))))) |
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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 (/ (+ (* -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))))))))) |
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(* (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))))))))) |
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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)) |
(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))))))) |
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(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))) |
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(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(*.f64 eps (fma.f64 eps (-.f64 (fma.f64 (cos.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (*.f64 eps (-.f64 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (*.f64 (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))))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (sin.f64 x)))) (sin.f64 x))))) (/.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (+.f64 (neg.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (sin.f64 x))) (/.f64 (*.f64 (*.f64 (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 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (*.f64 (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))))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (sin.f64 x)))) (sin.f64 x)))) (sin.f64 x)))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (cos.f64 x))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))) (/.f64 (*.f64 (*.f64 (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))))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (sin.f64 x)))) (sin.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (sin.f64 x)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
| 3 592× | lower-fma.f32 |
| 3 578× | lower-fma.f64 |
| 3 494× | lower-*.f32 |
| 3 478× | lower-*.f64 |
| 2 444× | lower-/.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 92 | 635 |
| 0 | 151 | 639 |
| 1 | 652 | 460 |
| 2 | 6392 | 460 |
| 0 | 8034 | 460 |
| 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)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps) |
#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(-.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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.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)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 eps eps) |
(cos.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 (*.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 (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 #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 (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 #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 -1/2 binary64)))) (fma.f64 eps #s(literal -1/6 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 (/.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 (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 #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 -1/2 binary64))))) (*.f64 eps #s(literal -1/6 binary64))) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 (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 #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 (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 #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 eps (-.f64 (/.f64 (+.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))) (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 eps (-.f64 (/.f64 (+.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))) (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 -1/2 binary64))) (fma.f64 eps #s(literal -1/6 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 (/.f64 (+.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))) (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))) eps (/.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 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 eps (-.f64 (/.f64 (+.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))) (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))))) |
(fma.f64 (-.f64 (/.f64 (+.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))) (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 -1/2 binary64))) eps (fma.f64 eps #s(literal -1/6 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 #s(literal 1 binary64) (/.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 (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 #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))))) |
(fma.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 eps (-.f64 (/.f64 (+.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))) (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))))) |
(fma.f64 (/.f64 #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 eps (-.f64 (/.f64 (+.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))) (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 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (-.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 (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 #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 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 (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 3 binary64)) (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 eps (-.f64 (/.f64 (+.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))) (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)) (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 (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 3 binary64)) (pow.f64 (*.f64 eps (-.f64 (/.f64 (+.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))) (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 3 binary64))) (fma.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (-.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 (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 #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 (*.f64 eps (-.f64 (/.f64 (+.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))) (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)))) |
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(fma.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (cos.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (tan.f64 x) #s(literal -1 binary64))) (*.f64 (tan.f64 x) (neg.f64 (tan.f64 (+.f64 eps x))))) |
(/.f64 (-.f64 (neg.f64 (tan.f64 (+.f64 eps x))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 eps x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))) (neg.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))) (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))) |
(pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))))) |
Compiled 56 145 to 3 724 computations (93.4% saved)
36 alts after pruning (31 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 313 | 14 | 1 327 |
| Fresh | 7 | 17 | 24 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 3 | 4 |
| Total | 1 324 | 36 | 1 360 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 60.1% | (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))) |
| 59.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) | |
| 32.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) | |
| ▶ | 58.7% | (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
| 59.1% | (/.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)))) | |
| 58.9% | (/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 27.2% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 59.9% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 60.1% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 59.8% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 59.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ✓ | 58.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
| 58.1% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) | |
| 98.0% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 97.7% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) | |
| ▶ | 97.9% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
| 97.8% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) | |
| ▶ | 97.6% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 98.0% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (pow.f64 x #s(literal 4 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)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 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)) | |
| 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| ▶ | 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
| 97.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 248/135 binary64)) #s(literal 17/9 binary64))) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 x (*.f64 x #s(literal 4/3 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)))) eps)) | |
| ✓ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
Compiled 1 704 to 876 computations (48.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (tan.f64 x) (tan.f64 eps)) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) | |
| cost-diff | 320 | (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))) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) (tan.f64 x)) | |
| cost-diff | 0 | (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) | |
| cost-diff | 1408 | (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) | |
| cost-diff | 8512 | (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 0 | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| cost-diff | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| cost-diff | 0 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| cost-diff | 0 | (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| cost-diff | 6464 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
| 14 048× | lower-fma.f32 |
| 14 032× | lower-fma.f64 |
| 4 538× | lower-*.f32 |
| 4 532× | lower-*.f64 |
| 2 890× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 729 |
| 0 | 131 | 706 |
| 1 | 267 | 696 |
| 2 | 650 | 652 |
| 3 | 1632 | 628 |
| 4 | 4399 | 628 |
| 0 | 8029 | 608 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
eps |
#s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(sin.f64 x) |
x |
(cos.f64 x) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(pow.f64 (cos.f64 x) #s(literal 3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) |
#s(literal 62/315 binary64) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
eps |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(tan.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
(tan.f64 x) |
x |
(tan.f64 eps) |
eps |
(+.f64 (tan.f64 x) (tan.f64 eps)) |
(neg.f64 (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.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)) |
(fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.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) |
(fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(fma.f64 eps #s(approx (+ (* 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))) (+.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 |
#s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
#s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(sin.f64 x) |
x |
(cos.f64 x) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
#s(literal 3 binary64) |
(pow.f64 (cos.f64 x) #s(literal 3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(tan.f64 x) |
#s(literal 2 binary64) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(*.f64 x (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))) x)) |
(*.f64 x x) |
x |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) |
#s(literal 62/315 binary64) |
#s(literal 17/45 binary64) |
#s(literal 2/3 binary64) |
#s(literal 1 binary64) |
eps |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) |
(+.f64 (/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(tan.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
eps |
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) |
(-.f64 (neg.f64 (tan.f64 x)) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
(neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))) |
#s(literal 1 binary64) |
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
(tan.f64 x) |
x |
(tan.f64 eps) |
eps |
(+.f64 (tan.f64 x) (tan.f64 eps)) |
(neg.f64 (tan.f64 x)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (*.f64 (tan.f64 x) (tan.f64 eps)) | |
| accuracy | 0.01171875 | (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) | |
| accuracy | 0.01171875 | (+.f64 (tan.f64 x) (tan.f64 eps)) | |
| accuracy | 25.526986305473354 | (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))) | |
| accuracy | 0.2421875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) | |
| accuracy | 0.25390625 | (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| accuracy | 0.3405075195368841 | (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) | |
| accuracy | 25.460744634376205 | (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) | |
| accuracy | 0.01953125 | (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) | |
| accuracy | 0.01953125 | (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) | |
| accuracy | 1.1777724581141595 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) | |
| accuracy | 1.2645734202701684 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) | |
| accuracy | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| accuracy | 0 | (*.f64 x x) | |
| accuracy | 1.2645734202701684 | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| accuracy | 1.641890407015841 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| accuracy | 0.02734375 | (pow.f64 (sin.f64 x) #s(literal 3 binary64)) | |
| accuracy | 0.12109375 | (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.8767330748578341 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| accuracy | 23.555289097224556 | #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
| 158.0ms | 100× | 1 | valid |
| 93.0ms | 154× | 0 | valid |
| 8.0ms | 2× | 3 | valid |
Compiled 521 to 76 computations (85.4% saved)
ival-mult: 60.0ms (26.8% of total)ival-div: 27.0ms (12.1% of total)ival-cos: 24.0ms (10.7% of total)ival-add: 23.0ms (10.3% of total)ival-pow2: 20.0ms (8.9% of total)adjust: 18.0ms (8.1% of total)const: 17.0ms (7.6% of total)ival-sub: 11.0ms (4.9% of total)ival-tan: 9.0ms (4% of total)ival-pow: 8.0ms (3.6% of total)ival-sin: 3.0ms (1.3% of total)ival-neg: 1.0ms (0.4% 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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))> |
#<alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))> |
#<alt (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)> |
#<alt (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))> |
#<alt #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))> |
#<alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)> |
#<alt #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))> |
#<alt (*.f64 x x)> |
#<alt #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))> |
#<alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)> |
#<alt #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))))> |
#<alt (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))> |
#<alt (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))> |
#<alt (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))))> |
#<alt (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64))> |
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 x))> |
#<alt (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)))> |
#<alt (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))> |
#<alt (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))> |
#<alt (*.f64 (tan.f64 x) (tan.f64 eps))> |
#<alt #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))> |
#<alt (pow.f64 (sin.f64 x) #s(literal 3 binary64))> |
#<alt (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))> |
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))> |
#<alt (+.f64 (tan.f64 x) (tan.f64 eps))> |
| Outputs |
|---|
#<alt (pow x 3)> |
#<alt (* (pow x 3) (+ 1 (pow x 2)))> |
#<alt (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))> |
#<alt (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<alt (/ (pow (sin x) 3) (pow (cos x) 3))> |
#<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)))> |
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#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<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 (* 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 (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)> |
#<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 (/ (sin eps) (cos eps))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
#<alt (+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<alt (/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps)))))> |
#<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 (* 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 (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)> |
#<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 (/ (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)) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (+ (* x (+ (* x (- (+ (* -1 (+ 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))))))) (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (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)))))))) (/ (* (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 (+ 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))))))))) (/ (* (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 x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x))> |
#<alt (/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x))> |
#<alt (/ (sin eps) (* x (cos eps)))> |
#<alt (/ (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x)> |
#<alt (/ (+ (* x (- (+ 1 (* x (- (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (* 1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x)> |
#<alt (/ (+ (* x (- (+ 1 (* x (- (+ (* x (- (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* 1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x)> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x)))> |
#<alt 1> |
#<alt (+ 1 (/ (* eps (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x)))> |
#<alt (+ 1 (* eps (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))))> |
#<alt (+ 1 (* eps (+ (* eps (- (+ 1 (* -1 (/ (* eps (* (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)))))))) (sin x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x)))> |
#<alt (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x)))> |
#<alt (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x)))> |
#<alt (/ (sin eps) (* x (cos eps)))> |
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) x)> |
#<alt (/ (+ (* x (- (* x (- (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (* 1/3 (/ (sin eps) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x)> |
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#<alt (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)> |
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#<alt (* eps (+ (* eps (- (+ 1 (* -1 (/ (* eps (* (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)))))))) (sin x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))> |
#<alt (* eps (+ (* eps (- (+ 1 (* eps (+ (* -1 (/ (* eps (* (cos x) (+ (* -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)))))) (sin x))) (* -1 (/ (* (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))))))) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))> |
#<alt (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)> |
#<alt (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)> |
#<alt (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)> |
#<alt (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)> |
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#<alt (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)> |
#<alt (/ 1 x)> |
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#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
#<alt (/ (cos x) (sin x))> |
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#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))> |
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#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))> |
#<alt 1> |
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#<alt 1> |
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#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))> |
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))> |
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#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))> |
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))> |
#<alt 1> |
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#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt 1> |
#<alt (+ 1 (* -1 (/ (* eps (sin x)) (cos x))))> |
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#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))> |
#<alt (/ (* x (sin eps)) (cos eps))> |
#<alt (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))> |
#<alt (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))> |
#<alt (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* eps (sin x)) (cos x))> |
#<alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))> |
#<alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))> |
#<alt (* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
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#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))> |
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#<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 (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> |
#<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 (/ (cos eps) (sin eps))> |
#<alt (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps)))> |
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))> |
#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))> |
#<alt (/ (cos x) (sin x))> |
#<alt (+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x)))> |
#<alt (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))> |
#<alt (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (+ eps x)) (sin (+ eps x)))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))> |
#<alt (/ (sin eps) (cos eps))> |
#<alt (+ x (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))> |
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (/ (sin x) (cos x))> |
#<alt (+ eps (/ (sin x) (cos x)))> |
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))> |
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))> |
126 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 5.0ms | x | @ | -inf | (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x))) |
| 4.0ms | eps | @ | 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)) eps) eps) |
| 3.0ms | x | @ | inf | (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x))) |
| 2.0ms | eps | @ | inf | (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x))) |
| 2.0ms | eps | @ | -inf | (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x))) |
| 1× | egg-herbie |
| 9 228× | lower-fma.f64 |
| 9 228× | lower-fma.f32 |
| 6 546× | lower-*.f64 |
| 6 546× | lower-*.f32 |
| 5 744× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 870 | 17748 |
| 1 | 2872 | 17095 |
| 0 | 8665 | 16453 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(pow x 3) |
(* (pow x 3) (+ 1 (pow x 2))) |
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2)))))) |
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2)))))))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/ (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))) |
(* 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 (+ (* 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 (+ 1 (+ (* 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 3) (- (+ 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 3) (- (+ 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 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (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 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (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 3) (- (+ 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 (* (pow eps 3) (+ (* -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 (* (pow eps 3) (+ (* -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 (/ (+ (* -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 (+ (* 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 (/ (+ (* -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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (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))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
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))) |
(* 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))) |
(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) |
(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) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
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))) |
(* 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))) |
(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 (* 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)))))) |
(/ (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)) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* x (- (+ (* -1 (+ 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))))))) (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1)) (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)))))))) (/ (* (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 (+ 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))))))))) (/ (* (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 x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x)) |
(/ (* (sin x) (- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1)) (cos x)) |
(/ (sin eps) (* x (cos eps))) |
(/ (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x) |
(/ (+ (* x (- (+ 1 (* x (- (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (* 1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x) |
(/ (+ (* x (- (+ 1 (* x (- (+ (* x (- (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* 1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) 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 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))) |
1 |
(+ 1 (/ (* eps (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) |
(+ 1 (* eps (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) |
(+ 1 (* eps (+ (* eps (- (+ 1 (* -1 (/ (* eps (* (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)))))))) (sin x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (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 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))) |
(/ (sin eps) (* x (cos eps))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) x) |
(/ (+ (* x (- (* x (- (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (* 1/3 (/ (sin eps) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x) |
(/ (+ (* x (- (* x (- (+ (* x (- (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) x) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- eps (* -1 x)))) (* (cos (- eps (* -1 x))) (sin x))) 1) |
(/ (* eps (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x)) |
(* eps (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) |
(* eps (+ (* eps (- (+ 1 (* -1 (/ (* eps (* (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)))))))) (sin x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) |
(* eps (+ (* eps (- (+ 1 (* eps (+ (* -1 (/ (* eps (* (cos x) (+ (* -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)))))) (sin x))) (* -1 (/ (* (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))))))) (sin x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (+ eps x))) (* (cos (+ eps x)) (sin x))) 1) |
(- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1) |
(- (/ (* (cos x) (sin (- x (* -1 eps)))) (* (cos (- x (* -1 eps))) (sin x))) 1) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (cos x) (sin x)) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x))) |
1 |
(+ 1 (/ (* x (sin eps)) (cos eps))) |
(+ 1 (* x (- (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)) (* -1 (/ (sin eps) (cos eps)))))) |
(+ 1 (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (sin eps) (cos eps)))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
1 |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(+ 1 (* eps (- (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) (* -1 (/ (sin x) (cos x)))))) |
(+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))) (* -1/3 (/ (sin x) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (sin x) (cos x)))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
1 |
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))) |
(+ 1 (* x (- (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))) |
(+ 1 (* x (- (* (pow x 2) (- (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
1 |
(+ 1 (* -1 (/ (* eps (sin x)) (cos x)))) |
(+ 1 (* eps (- (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))) |
(+ 1 (* eps (- (* (pow eps 2) (- (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) |
(/ (* x (sin eps)) (cos eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(+ (/ (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)))) |
(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 |
(+ 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)))))) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps 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 (- eps (* -1 x)))) |
(/ (cos x) (sin x)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (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 (- x (* -1 eps)))) |
(/ (sin eps) (cos eps)) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(/ (sin x) (cos x)) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
| Outputs |
|---|
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* (pow x 3) (+ 1 (pow x 2))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))) |
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2)))))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 11/15 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2)))))))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 88/189 binary64) #s(literal 11/15 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/ (pow (sin x) 3) (pow (cos x) 3)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 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 x (/.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 (* (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 x (sin.f64 eps)) (/.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)))) (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 (+.f64 #s(literal 1/2 binary64) (-.f64 (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) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (neg.f64 x) (/.f64 (*.f64 (sin.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))))) (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 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 (- 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 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))))) |
(*.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 eps (+.f64 (fma.f64 eps (-.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 eps (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+.f64 eps (*.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 eps (fma.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)))) (cos.f64 x))) (-.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 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))) |
(* eps (+ 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) (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 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 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 (+ (* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.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 (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 #s(literal 1/3 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 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 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 (+ (* 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))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.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 (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 #s(literal 1/3 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 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 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 (+ (* 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))))))))) |
(*.f64 (+.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 (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 #s(literal 1/3 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 eps (*.f64 eps eps))) |
(* (pow eps 3) (- (+ 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))))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.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 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps))))) (-.f64 #s(literal 1/3 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))))))) |
(* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (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 (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)))) (/.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))) (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 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ (/ 1 (pow eps 2)) (+ (/ (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 (*.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (+.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) eps)))) (/.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))) (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 3) (- (+ 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))))))))) |
(*.f64 (+.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 (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 #s(literal 1/3 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 eps (*.f64 eps eps))) |
(* -1 (* (pow eps 3) (+ (* -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))))) |
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 eps)) (+.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 (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 #s(literal 1/3 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))))))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -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 (/ (+ (* -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))))) |
(*.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps)) (+.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 (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 #s(literal 1/3 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))))))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -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 (/ (+ (* -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))))) |
(*.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps)) (+.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 (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 #s(literal 1/3 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))))))) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(+ eps (* 1/3 (pow eps 3))) |
(fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(fma.f64 x (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(fma.f64 x (fma.f64 x (*.f64 (*.f64 x (*.f64 eps eps)) #s(literal 4/3 binary64)) (*.f64 eps (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)) |
(+ eps (* eps (+ (* 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))))) |
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(+ eps (* eps (+ (* 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))))) |
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(/ (pow (sin x) 2) (pow (cos x) 2)) |
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(+ (* 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))) |
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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))))))))) |
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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 (/ (+ (* -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))))))))) |
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(* (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))))))))) |
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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)) |
(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))))))) |
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(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
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(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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eps |
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(pow x 2) |
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(/ (sin eps) (cos eps)) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
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(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
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(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
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(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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eps |
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(pow x 2) |
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(* 62/315 (pow x 8)) |
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(* 62/315 (pow x 8)) |
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(* (pow x 8) (+ 62/315 (* 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)))))) |
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(/ (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 x (/.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))) |
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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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(* -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)) |
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(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* (pow x 3) (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2)))) |
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(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| 4 440× | lower-fma.f32 |
| 4 424× | lower-fma.f64 |
| 4 098× | lower-*.f32 |
| 4 092× | lower-*.f64 |
| 2 650× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 641 |
| 0 | 131 | 606 |
| 1 | 641 | 497 |
| 2 | 5953 | 497 |
| 0 | 8170 | 489 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64))) |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (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))) |
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
#s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(pow.f64 (sin.f64 x) #s(literal 3 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(+.f64 (tan.f64 x) (tan.f64 eps)) |
| Outputs |
|---|
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 (neg.f64 (tan.f64 x))) #s(literal 3 binary64))) |
(exp.f64 (-.f64 (*.f64 #s(literal 3 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 3 binary64) (log.f64 (cos.f64 x))))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (tan.f64 x))) #s(literal 3/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (-.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x)))) #s(literal 3/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal 3 binary64)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (-.f64 (*.f64 #s(literal 3 binary64) (log.f64 (cos.f64 x))) (*.f64 #s(literal 3 binary64) (log.f64 (sin.f64 x)))) #s(literal -1 binary64))) |
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64))) |
(neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)))) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(/.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 3 binary64))) |
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) |
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) |
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (cos.f64 x)) |
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 3 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -3 binary64)) |
(pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) #s(literal -3/2 binary64)) |
(pow.f64 (exp.f64 (log.f64 (tan.f64 x))) #s(literal 3 binary64)) |
(pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal -3 binary64)))) |
(*.f64 (sin.f64 x) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal -3 binary64))) |
(*.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) |
(*.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (tan.f64 x)) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (neg.f64 (tan.f64 x))) |
(*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) |
(*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -3 binary64)))) |
(*.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) |
(*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) |
(*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal -3 binary64)))) |
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(*.f64 (/.f64 (sin.f64 x) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (sin.f64 x) (tan.f64 x))) |
(*.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)))) |
(*.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (cos.f64 x))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal 3/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3/2 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)) |
(+.f64 eps (*.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(+.f64 (*.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps) |
(-.f64 (/.f64 (pow.f64 (*.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 eps))) (/.f64 (*.f64 eps eps) (fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 eps)))) |
(fma.f64 eps (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) |
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(fma.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (tan.f64 eps)) |
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (tan.f64 eps)) |
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (tan.f64 eps) (tan.f64 x)) |
(fma.f64 (tan.f64 eps) #s(literal 1 binary64) (tan.f64 x)) |
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x)) |
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (tan.f64 eps)) |
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 eps)) |
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 eps)) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (tan.f64 eps)) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (tan.f64 eps))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal 1/2 binary64)) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) |
(/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (cos.f64 eps))) |
(/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (tan.f64 eps))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 eps) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 eps))) |
(/.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (cos.f64 eps) #s(literal 1 binary64))) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (fma.f64 (sin.f64 eps) (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 eps) (neg.f64 (cos.f64 x)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 (tan.f64 x) (tan.f64 eps))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 x) (tan.f64 eps)))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 eps) (tan.f64 x))) |
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (tan.f64 eps))) |
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64)) |
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 x) (tan.f64 eps)))) |
Compiled 38 607 to 2 650 computations (93.1% saved)
36 alts after pruning (28 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 152 | 6 | 1 158 |
| Fresh | 4 | 22 | 26 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 5 | 5 |
| Total | 1 158 | 36 | 1 194 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 60.1% | (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))) |
| 59.9% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) | |
| 21.7% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) | |
| 32.3% | (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) | |
| 59.3% | (/.f64 (-.f64 (/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| 59.1% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 27.2% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 59.9% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) | |
| 60.1% | (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| 59.8% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) | |
| ✓ | 59.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| ✓ | 59.9% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ✓ | 58.0% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
| 58.1% | (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) | |
| 98.0% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 97.7% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) | |
| ✓ | 97.9% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
| 97.8% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) | |
| ✓ | 97.6% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 98.0% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) | |
| 97.6% | #s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) | |
| 98.6% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (pow.f64 x #s(literal 4 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)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 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)) | |
| 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) | |
| 97.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 248/135 binary64)) #s(literal 17/9 binary64))) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 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)))) eps)) | |
| 98.5% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 x (*.f64 x #s(literal 4/3 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)))) eps)) | |
| ✓ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
Compiled 2 261 to 735 computations (67.5% saved)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
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#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
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#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
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(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
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(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
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(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 #s(approx (* 1 (/ 1 (tan x))) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
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(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.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))) |
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 x (*.f64 x #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 248/135 binary64)) #s(literal 17/9 binary64))) #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (pow.f64 x #s(literal 4 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (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 #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)) (/.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 |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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)) |
3 calls:
| 30.0ms | eps |
| 18.0ms | x |
| 16.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 (-.f64 (/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 #s(approx (* 1 (/ 1 (tan x))) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.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))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.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))) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.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)))) |
#s(approx (- (tan (+ x eps)) (tan 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 x (*.f64 x #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/9 binary64)) #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 248/135 binary64)) #s(literal 17/9 binary64))) #s(literal 4/3 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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (pow.f64 x #s(literal 4 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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (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)))) #s(approx (pow (* (sin x) (tan x)) 2) (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 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)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) |
3 calls:
| 32.0ms | x |
| 17.0ms | eps |
| 15.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 (-.f64 (/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 #s(approx (* 1 (/ 1 (tan x))) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.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))) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) |
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64)))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.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))) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.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)))) |
#s(approx (- (tan (+ x eps)) (tan 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 |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 29.0ms | eps |
| 14.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 14.0ms | 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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 eps #s(literal 1/3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))) |
(/.f64 (-.f64 (/.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))) (sin.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 x eps))))) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 #s(approx (* 1 (/ 1 (tan x))) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
3 calls:
| 14.0ms | eps |
| 11.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 11.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | eps |
| 98.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
3 calls:
| 9.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 1 | x |
| 98.0% | 1 | eps |
| 98.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
3 calls:
| 36.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 1 | x |
| 98.0% | 1 | eps |
| 98.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)) x))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64))))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
3 calls:
| 34.0ms | x |
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
| 97.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (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)) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
3 calls:
| 5.0ms | eps |
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | x |
| 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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
3 calls:
| 5.0ms | x |
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | 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 |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* 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)) (fma.f64 x eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal 1/3 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* 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)) eps) eps) (fma.f64 x (*.f64 eps eps) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) eps)))) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
3 calls:
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | eps |
| 3.0ms | 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)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| Outputs |
|---|
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
3 calls:
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | x |
| 1.0ms | eps |
| 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)
| 1× | egg-herbie |
| 24× | *-commutative_binary64 |
| 24× | +-commutative_binary64 |
| 12× | sub-neg_binary64 |
| 8× | neg-sub0_binary64 |
| 8× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 134 | 627 |
| 1 | 158 | 627 |
| 2 | 172 | 627 |
| 3 | 180 | 627 |
| 4 | 185 | 627 |
| 5 | 186 | 627 |
| 1× | saturated |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (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)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #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)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 #s(approx (+ (* 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))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps #s(approx (+ (* 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))) (fma.f64 eps #s(literal 1/3 binary64) x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x 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 eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64))))) eps eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))) eps)) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (*.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))))) |
#s(approx (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ x eps))) 1)) (* (/ 1 (tan (+ x eps))) (/ 1 (tan x)))) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 14 592× | lower-fma.f64 |
| 14 592× | lower-fma.f32 |
| 9 474× | lower-fma.f64 |
| 9 474× | lower-fma.f32 |
| 9 410× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 746 | 14389 |
| 1 | 2391 | 13723 |
| 0 | 8282 | 13377 |
| 0 | 82 | 641 |
| 0 | 131 | 606 |
| 1 | 641 | 497 |
| 2 | 5953 | 497 |
| 0 | 8170 | 489 |
| 0 | 57 | 462 |
| 0 | 106 | 417 |
| 1 | 488 | 311 |
| 2 | 4317 | 303 |
| 0 | 9260 | 293 |
| 0 | 157 | 1351 |
| 1 | 464 | 1285 |
| 2 | 1534 | 1274 |
| 3 | 5949 | 1242 |
| 0 | 8534 | 1195 |
| 0 | 92 | 635 |
| 0 | 151 | 639 |
| 1 | 652 | 460 |
| 2 | 6392 | 460 |
| 0 | 8034 | 460 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6117 | 16 |
| 0 | 8095 | 16 |
| 0 | 855 | 18952 |
| 1 | 2820 | 18177 |
| 0 | 8817 | 17593 |
| 1× | fuel |
| 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 498 to 241 computations (51.6% saved)
Compiled 540 to 196 computations (63.7% saved)
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