Details

analyze824.0ms (8.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample76.0ms (0.8%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	128	valid
6.0ms	32×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify365.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (195.0ms)

Iter	Nodes	Cost
0	5740	19

prune10.0ms (0.1%)

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

Merged error: 33.3b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_425`
22×	`log-pow_binary64_508`
21×	`pow1_binary64_480`
17×	`add-sqr-sqrt_binary64_441`
16×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `associate-/l*_binary64_364`
5×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`sqrt-div_binary64_436` `associate-/r*_binary64_363`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435`
2×	`log-div_binary64_506` `div-sub_binary64_424`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

3 → 74

Calls

3 calls:

15.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
9.0ms	(+.f64 (.f64 re re) (.f64 im im))

series260.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

170.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
54.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
36.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5313	1833

prune195.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	70	15	85

Merged error: 9.0b

Counts

85 → 15

Compiler

Compiled 1842 to 491 computations (73.3% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`sqrt-div_binary64_436`
7×	`pow1_binary64_480`
6×	`cbrt-prod_binary64_450`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`cbrt-div_binary64_451`
1×	`pow1/3_binary64_501`

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series257.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify170.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4902	1087
1	4902	1087

prune174.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	73	15	88

Merged error: 9.0b

Counts

88 → 15

Compiler

Compiled 3012 to 636 computations (78.9% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.1b	(pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 1/3)
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_441`
12×	`sqrt-prod_binary64_435`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`pow1_binary64_480`
6×	`sqrt-div_binary64_436` `unpow-prod-down_binary64_498`
5×	`add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `pow1/2_binary64_499` `add-cbrt-cube_binary64_455` `sqrt-pow1_binary64_437`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow-pow_binary64_491` `pow-unpow_binary64_496` `rem-sqrt-square_binary64_432`
1×	`unpow1/3_binary64_486` `sqrt-pow2_binary64_438` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488`

Counts

4 → 69

Calls

4 calls:

11.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 1/3)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series259.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) 1/3)
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify158.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4847	1115
1	4847	1115

prune195.0ms (2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	81	15	96

Merged error: 9.0b

Counts

96 → 15

Compiler

Compiled 3288 to 751 computations (77.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
32.1b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_425`
72×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
47×	`pow1_binary64_480`
43×	`log-pow_binary64_508`
24×	`associate-/r*_binary64_363`
12×	`add-exp-log_binary64_457`
11×	`add-cbrt-cube_binary64_455`
7×	`associate-/l*_binary64_364`
6×	`add-log-exp_binary64_458` `div-inv_binary64_416`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`log-prod_binary64_505`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393` `log-div_binary64_506`
1×	`rem-log-exp_binary64_460` `sum-log_binary64_510` `associate-/r/_binary64_365` `+-commutative_binary64_349`

Counts

4 → 159

Calls

4 calls:

14.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
8.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(+.f64 (.f64 re re) (.f64 im im))
7.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series516.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
199.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
56.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
34.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify172.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5141	4862

prune257.0ms (2.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	2	10	12
Picked	1	0	1
Done	0	2	2
Total	168	18	186

Merged error: 9.0b

Counts

186 → 18

Compiler

Compiled 3885 to 952 computations (75.5% saved)

regimes1.5s (14.8%)

Compiler: Compiled 5136 to 3301 computations (35.7% saved)

bsearch322.0ms (3.2%)

Steps

Iters	Range		Point
8	3.223629475968693e+100	5.1538587234692174e+103	2.823860171713815e+101
6	9.577442542548388e-165	5.807652413671839e-164	2.8627681168693353e-164
5	1.2033697886205157e-253	4.596036591901927e-253	2.877179155462273e-253
8	-1.6154390749362116e+106	-2.1945448997525985e+102	-1.3631295677911341e+106

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	156
1	43	156

end0.0ms (0%)

sample3.8s (38.2%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
175.0ms	978×	body	128	nan

Compiler

Compiled 1141 to 703 computations (38.4% saved)

Details

analyze824.0ms (8.3%)

sample76.0ms (0.8%)

simplify365.0ms (3.7%)

prune10.0ms (0.1%)

localize22.0ms (0.2%)

rewrite45.0ms (0.4%)

series260.0ms (2.6%)

simplify146.0ms (1.5%)

prune195.0ms (2%)

localize31.0ms (0.3%)

rewrite49.0ms (0.5%)

series257.0ms (2.6%)

simplify170.0ms (1.7%)

prune174.0ms (1.7%)

localize36.0ms (0.4%)

rewrite49.0ms (0.5%)

series259.0ms (2.6%)

simplify158.0ms (1.6%)

prune195.0ms (2%)

localize23.0ms (0.2%)

rewrite67.0ms (0.7%)

series516.0ms (5.2%)

simplify172.0ms (1.7%)

prune257.0ms (2.6%)

regimes1.5s (14.8%)

bsearch322.0ms (3.2%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.8s (38.2%)

Profiling