Details

analyze519.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample104.0ms (0.3%)

Algorithm

1×

intervals

Results

49.0ms	52×	body	2048	valid
31.0ms	105×	body	1024	valid
10.0ms	57×	body	512	valid
3.0ms	22×	body	256	valid
2.0ms	2×	body	4096	valid
1.0ms	18×	body	128	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	172	6
1	172	6

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

Counts

2 → 2

Compiler

Compiled 4 to 4 computations (0% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 1 (cos.f64 x))
0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
1.8b	(-.f64 1 (cos.f64 x))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
18×	`times-frac_binary64_425`
14×	`add-cube-cbrt_binary64_454`
10×	`difference-of-squares_binary64_388`
6×	`associate-/l*_binary64_364`
5×	`distribute-lft-out--_binary64_371`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`cancel-sign-sub-inv_binary64_385` `associate-/r*_binary64_363`
2×	`flip3--_binary64_423` `flip--_binary64_394` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `hang-p0-tan_binary64_542` `div-inv_binary64_416` `frac-2neg_binary64_430` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

2 → 60

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
5.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
0.0ms	(-.f64 1 (cos.f64 x))

series56.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

38.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
17.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 125 to 108 computations (13.6% saved)

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5124	995

localize7.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune250.0ms (0.7%)

Pruning

45 alts after pruning (43 fresh and 2 done)

	Pruned	Kept	Total
New	25	43	68
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	25	45	70

Error

Counts

70 → 45

Compiler

Compiled 1227 to 782 computations (36.3% saved)

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

17.1b	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))
0.4b	(pow.f64 (tan.f64 (/.f64 x 2)) 3)
0.4b	(pow.f64 (tan.f64 (/.f64 x 2)) 3)
17.1b	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_450`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
6×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
3×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow-unpow_binary64_496` `pow1_binary64_480`
2×	`add-log-exp_binary64_458` `unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391` `cube-div_binary64_448` `tan-quot_binary64_578`
1×	`pow1/3_binary64_501` `cbrt-div_binary64_451` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `pow-pow_binary64_491`

Counts

2 → 46

Calls

4 calls:

4.0ms	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))
3.0ms	(pow.f64 (tan.f64 (/.f64 x 2)) 3)
0.0ms	(pow.f64 (tan.f64 (/.f64 x 2)) 3)
0.0ms	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))

series119.0ms (0.3%)

Counts

2 → 8

Calls

2 calls:

77.0ms	(pow.f64 (tan.f64 (/.f64 x 2)) 3)
42.0ms	(cbrt.f64 (pow.f64 (tan.f64 (/.f64 x 2)) 3))

Compiler

Compiled 155 to 141 computations (9% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5556	634

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (sin.f64 x)))
0.1b	(/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))
0.0b	(sqrt.f64 (sin.f64 x))
0.0b	(sqrt.f64 (sin.f64 x))
0.1b	(/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))
0.1b	(/.f64 1 (sqrt.f64 (sin.f64 x)))
0.1b	(*.f64 (/.f64 1 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x))))
1.8b	(-.f64 1 (cos.f64 x))

rewrite71.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

161×	`add-sqr-sqrt_binary64_441`
130×	`times-frac_binary64_425`
121×	`*-un-lft-identity_binary64_419`
73×	`add-cube-cbrt_binary64_454`
71×	`sqrt-prod_binary64_435`
40×	`associate-r_binary64_359`
32×	`add-exp-log_binary64_457`
28×	`difference-of-squares_binary64_388`
22×	`associate-l_binary64_360`
20×	`add-cbrt-cube_binary64_455`
15×	`unswap-sqr_binary64_387`
14×	`distribute-lft-out--_binary64_371`
12×	`associate-/r*_binary64_363`
11×	`div-exp_binary64_470`
9×	`associate-/l*_binary64_364`
8×	`prod-exp_binary64_468` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `cbrt-undiv_binary64_453`
4×	`div-inv_binary64_416` `cbrt-unprod_binary64_452`
3×	`1-exp_binary64_463` `rec-exp_binary64_469` `pow-flip_binary64_493` `cancel-sign-sub-inv_binary64_385`
2×	`clear-num_binary64_418` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `sub-neg_binary64_412` `inv-pow_binary64_504` `pow1/2_binary64_499` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `div-sub_binary64_424`

Counts

4 → 226

Calls

8 calls:

30.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x))))
8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))
4.0ms	(/.f64 1 (sqrt.f64 (sin.f64 x)))
4.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(sqrt.f64 (sin.f64 x))

series151.0ms (0.4%)

Counts

4 → 13

Calls

4 calls:

56.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))
44.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x))))
31.0ms	(/.f64 1 (sqrt.f64 (sin.f64 x)))
19.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 329 to 265 computations (19.5% saved)

simplify110.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4980	4372
1	4980	4372

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x)))
0.2b	(.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x))
0.2b	(*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))
0.1b	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))
0.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x)))
0.4b	(pow.f64 (cos.f64 x) 3)
0.5b	(+.f64 1 (cos.f64 x))
1.6b	(-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-sqr-sqrt_binary64_441`
72×	`difference-of-squares_binary64_388`
71×	`*-un-lft-identity_binary64_419`
60×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
34×	`times-frac_binary64_425` `associate-/l*_binary64_364`
32×	`sqr-pow_binary64_391`
18×	`distribute-lft-out--_binary64_371`
12×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458`
5×	`cube-mult_binary64_449` `pow1_binary64_480`
3×	`difference-cubes_binary64_421` `pow-unpow_binary64_496`
2×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `unpow3_binary64_485` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `rem-cube-cbrt_binary64_442` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `diff-log_binary64_511` `associate-/r*_binary64_363` `+-commutative_binary64_349` `div-sub_binary64_424`

Counts

4 → 177

Calls

8 calls:

22.0ms	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x)))
17.0ms	(-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3))
4.0ms	(+.f64 1 (cos.f64 x))
2.0ms	(pow.f64 (cos.f64 x) 3)
0.0ms	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))

series246.0ms (0.7%)

Counts

4 → 16

Calls

4 calls:

149.0ms	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x)))
43.0ms	(-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3))
34.0ms	(pow.f64 (cos.f64 x) 3)
21.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 563 to 441 computations (21.7% saved)

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5067	4232

prune4.0s (11.2%)

Pruning

213 alts after pruning (208 fresh and 5 done)

	Pruned	Kept	Total
New	309	177	486
Fresh	7	31	38
Picked	0	0	0
Done	2	5	7
Total	318	213	531

Error

Counts

531 → 213

Compiler

Compiled 9883 to 6266 computations (36.6% saved)

localize7.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (cos.f64 x) 2)
0.2b	(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
0.2b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x))
0.1b	(+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))
0.3b	(pow.f64 (cos.f64 x) 2)
0.4b	(pow.f64 (cos.f64 x) 3)
0.6b	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))
1.6b	(-.f64 1 (pow.f64 (cos.f64 x) 3))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_441`
21×	`*-un-lft-identity_binary64_419`
12×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
11×	`unpow-prod-down_binary64_498`
8×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `cube-prod_binary64_447`
6×	`add-exp-log_binary64_457` `pow-unpow_binary64_496` `pow1_binary64_480`
5×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455`
3×	`unpow2_binary64_484`
2×	`unpow3_binary64_485` `cube-mult_binary64_449` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `pow-pow_binary64_491`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `distribute-rgt1-in_binary64_375` `rem-cube-cbrt_binary64_442` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `distribute-rgt-out_binary64_372` `+-commutative_binary64_349`

Counts

4 → 87

Calls

8 calls:

7.0ms	(-.f64 1 (pow.f64 (cos.f64 x) 3))
5.0ms	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))
2.0ms	(pow.f64 (cos.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 3)
0.0ms	(+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))

series122.0ms (0.3%)

Counts

4 → 14

Calls

4 calls:

41.0ms	(-.f64 1 (pow.f64 (cos.f64 x) 3))
38.0ms	(pow.f64 (cos.f64 x) 3)
25.0ms	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))
18.0ms	(pow.f64 (cos.f64 x) 2)

Compiler

Compiled 510 to 393 computations (22.9% saved)

simplify81.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5093	1007

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (-.f64 (pow.f64 1 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3))) (.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x)))
0.2b	(.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x))
0.2b	(*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))
0.1b	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))
0.4b	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
0.4b	(pow.f64 (cos.f64 x) 3)
0.5b	(+.f64 1 (cos.f64 x))
1.6b	(-.f64 (pow.f64 1 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`add-sqr-sqrt_binary64_441`
97×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
90×	`cbrt-prod_binary64_450`
66×	`difference-of-squares_binary64_388`
49×	`*-un-lft-identity_binary64_419`
36×	`sqr-pow_binary64_391`
33×	`cancel-sign-sub-inv_binary64_385`
22×	`add-cube-cbrt_binary64_454`
8×	`add-log-exp_binary64_458` `cube-mult_binary64_449`
7×	`unpow3_binary64_485` `add-exp-log_binary64_457`
6×	`add-cbrt-cube_binary64_455` `pow-unpow_binary64_496`
5×	`pow-exp_binary64_487` `pow1_binary64_480`
3×	`pow-to-exp_binary64_488`
2×	`rem-cube-cbrt_binary64_442` `distribute-lft-out--_binary64_371` `pow-pow_binary64_491`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `flip3--_binary64_423` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 190

Calls

8 calls:

30.0ms	(-.f64 (pow.f64 1 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))
5.0ms	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
4.0ms	(+.f64 1 (cos.f64 x))
2.0ms	(pow.f64 (cos.f64 x) 3)
0.0ms	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))

series155.0ms (0.4%)

Counts

4 → 16

Calls

4 calls:

54.0ms	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
52.0ms	(-.f64 (pow.f64 1 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))
32.0ms	(pow.f64 (cos.f64 x) 3)
17.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 665 to 534 computations (19.7% saved)

simplify98.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5205	2658

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 (pow.f64 1 (/.f64 3 2)) (sqrt.f64 (pow.f64 (cos.f64 x) 3))) (*.f64 (/.f64 (sin.f64 x) (-.f64 1 (sqrt.f64 (pow.f64 (cos.f64 x) 3)))) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
0.1b	(+.f64 (pow.f64 1 (/.f64 3 2)) (sqrt.f64 (pow.f64 (cos.f64 x) 3)))
0.0b	(sqrt.f64 (pow.f64 (cos.f64 x) 3))
0.0b	(sqrt.f64 (pow.f64 (cos.f64 x) 3))
0.4b	(pow.f64 (cos.f64 x) 3)
0.4b	(pow.f64 (cos.f64 x) 3)
0.6b	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))
1.7b	(-.f64 1 (sqrt.f64 (pow.f64 (cos.f64 x) 3)))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_441`
25×	`*-un-lft-identity_binary64_419`
21×	`sqrt-prod_binary64_435`
15×	`cancel-sign-sub-inv_binary64_385`
14×	`add-cube-cbrt_binary64_454`
11×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
10×	`difference-of-squares_binary64_388`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow-unpow_binary64_496` `pow1_binary64_480`
5×	`sqr-pow_binary64_391`
3×	`unpow3_binary64_485` `cube-mult_binary64_449`
2×	`rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `unpow2_binary64_484`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `distribute-rgt1-in_binary64_375` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `flip3--_binary64_423` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `distribute-rgt-out_binary64_372` `+-commutative_binary64_349`

Counts

4 → 98

Calls

8 calls:

8.0ms	(-.f64 1 (sqrt.f64 (pow.f64 (cos.f64 x) 3)))
6.0ms	(pow.f64 (cos.f64 x) 3)
6.0ms	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))
2.0ms	(pow.f64 (cos.f64 x) 3)
0.0ms	(sqrt.f64 (pow.f64 (cos.f64 x) 3))

series160.0ms (0.4%)

Counts

4 → 14

Calls

4 calls:

58.0ms	(-.f64 1 (sqrt.f64 (pow.f64 (cos.f64 x) 3)))
41.0ms	(pow.f64 (cos.f64 x) 3)
34.0ms	(pow.f64 (cos.f64 x) 3)
27.0ms	(+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))

Compiler

Compiled 847 to 678 computations (20% saved)

simplify80.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5003	1255

prune5.6s (15.6%)

Pruning

320 alts after pruning (310 fresh and 10 done)

	Pruned	Kept	Total
New	307	112	419
Fresh	5	198	203
Picked	0	0	0
Done	0	10	10
Total	312	320	632

Error

Counts

632 → 320

Compiler

Compiled 12821 to 9045 computations (29.5% saved)

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(*.f64 1/24 (pow.f64 x 3))
0.3b	(*.f64 1/24 (pow.f64 x 3))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64_359` `add-sqr-sqrt_binary64_441`
6×	`add-exp-log_binary64_457`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`unpow-prod-down_binary64_498` `unswap-sqr_binary64_387` `cube-prod_binary64_447`
3×	`prod-exp_binary64_468` `associate-l_binary64_360` `add-cbrt-cube_binary64_455`
2×	`sqr-pow_binary64_391`
1×	`add-log-exp_binary64_458` `unpow3_binary64_485` `cube-mult_binary64_449` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `*-commutative_binary64_350` `pow1_binary64_480`

Counts

1 → 31

Calls

2 calls:

6.0ms	(*.f64 1/24 (pow.f64 x 3))
0.0ms	(*.f64 1/24 (pow.f64 x 3))

series30.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

30.0ms

(*.f64 1/24 (pow.f64 x 3))

Compiler

Compiled 54 to 48 computations (11.1% saved)

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4921	305
1	4921	305

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 (cos.f64 x)))
0.3b	(cbrt.f64 (-.f64 1 (cos.f64 x)))
0.2b	(/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x)))))
0.2b	(/.f64 (sin.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x))))
0.3b	(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x))))
1.8b	(-.f64 1 (cos.f64 x))
1.8b	(-.f64 1 (cos.f64 x))
1.8b	(-.f64 1 (cos.f64 x))

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_441`
42×	`*-un-lft-identity_binary64_419`
32×	`cbrt-prod_binary64_450`
15×	`add-cube-cbrt_binary64_454`
14×	`difference-of-squares_binary64_388`
12×	`cbrt-div_binary64_451`
11×	`swap-sqr_binary64_386` `pow1_binary64_480`
10×	`add-log-exp_binary64_458`
9×	`associate-r_binary64_359` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `associate-l_binary64_360` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
6×	`pow1/3_binary64_501` `add-exp-log_binary64_457`
4×	`unswap-sqr_binary64_387` `frac-times_binary64_429` `add-cbrt-cube_binary64_455`
3×	`sub-neg_binary64_412` `diff-log_binary64_511`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 110

Calls

8 calls:

12.0ms	(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x))))
4.0ms	(-.f64 1 (cos.f64 x))
4.0ms	(-.f64 1 (cos.f64 x))
4.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(/.f64 (sin.f64 x) (cbrt.f64 (-.f64 1 (cos.f64 x))))

series160.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x))))
17.0ms	(-.f64 1 (cos.f64 x))
17.0ms	(-.f64 1 (cos.f64 x))
16.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 507 to 401 computations (20.9% saved)

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4884	1684
1	4884	1684

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (+.f64 1 (.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))) (sin.f64 x))
0.2b	(*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 x) 6))
0.2b	(*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)))
0.1b	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))
0.4b	(pow.f64 (cos.f64 x) 3)
0.5b	(+.f64 1 (cos.f64 x))
0.6b	(pow.f64 (cos.f64 x) 6)
1.6b	(-.f64 (pow.f64 1 3) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 x) 6))))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_441`
17×	`*-un-lft-identity_binary64_419`
10×	`add-cube-cbrt_binary64_454`
8×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458`
6×	`difference-of-squares_binary64_388` `add-exp-log_binary64_457` `pow-unpow_binary64_496` `pow1_binary64_480`
5×	`cube-prod_binary64_447` `add-cbrt-cube_binary64_455`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`sqr-pow_binary64_391`
2×	`cube-mult_binary64_449` `pow-exp_binary64_487` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `pow-pow_binary64_491`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `unpow3_binary64_485` `rem-cube-cbrt_binary64_442` `cbrt-prod_binary64_450` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `flip3--_binary64_423` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 75

Calls

8 calls:

8.0ms	(-.f64 (pow.f64 1 3) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 x) 6))))
4.0ms	(+.f64 1 (cos.f64 x))
2.0ms	(pow.f64 (cos.f64 x) 3)
2.0ms	(pow.f64 (cos.f64 x) 6)
0.0ms	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))

series150.0ms (0.4%)

Counts

4 → 16

Calls

4 calls:

53.0ms	(pow.f64 (cos.f64 x) 6)
43.0ms	(-.f64 (pow.f64 1 3) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 x) 6))))
37.0ms	(pow.f64 (cos.f64 x) 3)
17.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 742 to 569 computations (23.3% saved)

simplify68.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4934	875
1	4934	875

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (sin.f64 x)))
0.0b	(sqrt.f64 (sin.f64 x))
0.0b	(sqrt.f64 (sin.f64 x))
0.0b	(sqrt.f64 (sin.f64 x))
0.1b	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
0.1b	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
0.3b	(.f64 (.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x)))))
1.8b	(-.f64 1 (cos.f64 x))

rewrite86.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`sqrt-prod_binary64_435`
162×	`times-frac_binary64_425`
127×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
124×	`add-cube-cbrt_binary64_454`
87×	`cbrt-prod_binary64_450`
58×	`associate-r_binary64_359`
29×	`add-exp-log_binary64_457`
18×	`add-cbrt-cube_binary64_455` `associate-/r*_binary64_363`
12×	`associate-/l*_binary64_364`
10×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`pow1_binary64_480`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
2×	`clear-num_binary64_418` `difference-of-squares_binary64_388` `frac-2neg_binary64_430`
1×	`associate-l/_binary64_362` `sub-neg_binary64_412` `frac-times_binary64_429` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `-commutative_binary64_350` `associate-l_binary64_360` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 263

Calls

8 calls:

25.0ms	(.f64 (.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x)))))
6.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
6.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
4.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(sqrt.f64 (sin.f64 x))

series225.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
81.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))
35.0ms	(.f64 (.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (sqrt.f64 (sin.f64 x)))))
20.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 576 to 441 computations (23.4% saved)

simplify125.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4912	5976
1	4912	5976

prune14.3s (39.6%)

Pruning

463 alts after pruning (448 fresh and 15 done)

	Pruned	Kept	Total
New	371	151	522
Fresh	8	297	305
Picked	0	0	0
Done	0	15	15
Total	379	463	842

Error

Counts

842 → 463

Compiler

Compiled 8750 to 4970 computations (43.2% saved)

simplify510.0ms (1.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5060	29131

regimes3.0s (8.2%)

Compiler: Compiled 28728 to 20788 computations (27.6% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.1%)

Compiler: Compiled 30 to 27 computations (10% saved)

bsearch46.0ms (0.1%)

Steps

Iters	Range		Point
10	6.436151519445615e-09	49331.83600018016	3.146923069917702
10	-502011.5844155214	-6.244221140042407e-05	-3.17141691731626

Compiler

Compiled 1 to 1 computations (0% saved)

regimes21.0ms (0.1%)

Compiler: Compiled 8 to 11 computations (-37.5% saved)

bsearch42.0ms (0.1%)

Steps

Iters	Range		Point
10	6.436151519445615e-09	49331.83600018016	1.4037561512157106
10	-502011.5844155214	-6.244221140042407e-05	-3.17141691731626

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0%)

Compiler: Compiled 39 to 33 computations (15.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	55
1	35	55

end0.0ms (0%)

sample4.3s (12%)

Algorithm

1×

intervals

Results

2.2s	2025×	body	2048	valid
923.0ms	2978×	body	1024	valid
276.0ms	1489×	body	512	valid
97.0ms	771×	body	256	valid
90.0ms	92×	body	4096	valid
49.0ms	643×	body	128	valid
4.0ms	2×	body	8192	valid

Compiler

Compiled 14434 to 10453 computations (27.6% saved)