Details

analyze412.0ms (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)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
2.0ms	26×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify190.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5740	19

prune8.0ms (0.2%)

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

31.3b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize11.0ms (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))
29.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms (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:

7.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series148.0ms (3%)

Counts

3 → 9

Calls

3 calls:

97.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
26.0ms	(+.f64 (.f64 re re) (.f64 im im))
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5313	1833

prune101.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	15	83
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	15	85

Error

7.7b

Counts

85 → 15

Compiler

Compiled 1817 to 474 computations (73.9% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
30.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64_425`
14×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow1_binary64_480`
11×	`log-pow_binary64_508`
6×	`add-exp-log_binary64_457`
5×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
4×	`associate-/r_binary64_363` `log-div_binary64_506` `associate-/l_binary64_364`
3×	`flip3-+_binary64_422` `log-prod_binary64_505` `flip-+_binary64_393`
2×	`div-sub_binary64_424`
1×	`clear-num_binary64_418` `rem-log-exp_binary64_460` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

3 → 63

Calls

3 calls:

7.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series140.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
33.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5558	1536

prune72.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	6	8	14
Picked	0	1	1
Done	0	0	0
Total	75	12	87

Error

7.7b

Counts

87 → 12

Compiler

Compiled 1630 to 520 computations (68.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1 (log.f64 base))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
29.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_441`
26×	`times-frac_binary64_425`
24×	`*-un-lft-identity_binary64_419`
23×	`add-cube-cbrt_binary64_454`
17×	`add-exp-log_binary64_457` `pow1_binary64_480`
16×	`associate-r_binary64_359`
11×	`add-cbrt-cube_binary64_455`
10×	`log-pow_binary64_508`
6×	`add-log-exp_binary64_458` `associate-l_binary64_360`
4×	`prod-exp_binary64_468` `associate-/r*_binary64_363` `div-exp_binary64_470`
3×	`unswap-sqr_binary64_387` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `1-exp_binary64_463` `pow1/2_binary64_499` `div-inv_binary64_416` `cbrt-unprod_binary64_452` `rec-exp_binary64_469` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `inv-pow_binary64_504` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `pow-flip_binary64_493` `un-div-inv_binary64_417` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 103

Calls

4 calls:

10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(/.f64 1 (log.f64 base))

series223.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
76.0ms	(/.f64 1 (log.f64 base))
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5000	1782

prune102.0ms (2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	112	15	127

Error

7.7b

Counts

127 → 15

Compiler

Compiled 2307 to 728 computations (68.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
0.7b	(log.f64 (exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))))
29.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`log-pow_binary64_508`
72×	`times-frac_binary64_425`
56×	`exp-prod_binary64_471`
51×	`pow1_binary64_480`
41×	`add-sqr-sqrt_binary64_441`
40×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
14×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
8×	`sqrt-div_binary64_436` `log-div_binary64_506`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/l*_binary64_364` `div-sub_binary64_424`
5×	`add-log-exp_binary64_458` `div-inv_binary64_416`
4×	`flip3-+_binary64_422` `exp-diff_binary64_467` `flip-+_binary64_393` `associate-/r*_binary64_363`
3×	`log-prod_binary64_505` `sqrt-prod_binary64_435`
2×	`exp-to-pow_binary64_481`
1×	`clear-num_binary64_418` `rem-log-exp_binary64_460` `frac-2neg_binary64_430` `rem-exp-log_binary64_459` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 145

Calls

4 calls:

8.0ms	(log.f64 (exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))))
8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
7.0ms	(exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series393.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(log.f64 (exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))))
132.0ms	(exp.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)))
98.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4907	3287
1	4907	3287

prune126.0ms (2.5%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	152	5	157
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	153	19	172

Error

7.6b

Counts

172 → 19

Compiler

Compiled 3349 to 622 computations (81.4% saved)

regimes637.0ms (12.8%)

Accuracy

Total 10.2b remaining (59.2%)

Threshold costs 0b (0%)

Compiler

Compiled 4226 to 2701 computations (36.1% saved)

bsearch66.0ms (1.3%)

Steps

Iters	Range		Point
4	3.9929935067499496e+124	7.24706212544778e+124	7.137942334441359e+124
7	-1.3869787531766102e+93	-9.997196574194931e+90	-4.624380692152419e+91

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	70
1	36	70

end0.0ms (0%)

sample1.9s (37.2%)

Algorithm

1×

intervals

Results

786.0ms	8000×	body	128	valid
104.0ms	1103×	body	128	nan

Compiler

Compiled 905 to 576 computations (36.4% saved)

Details

analyze412.0ms (8.3%)

sample37.0ms (0.7%)

simplify190.0ms (3.8%)

prune8.0ms (0.2%)

localize11.0ms (0.2%)

rewrite21.0ms (0.4%)

series148.0ms (3%)

simplify81.0ms (1.6%)

prune101.0ms (2%)

localize14.0ms (0.3%)

rewrite20.0ms (0.4%)

series140.0ms (2.8%)

simplify65.0ms (1.3%)

prune72.0ms (1.4%)

localize12.0ms (0.2%)

rewrite29.0ms (0.6%)

series223.0ms (4.5%)

simplify73.0ms (1.5%)

prune102.0ms (2%)

localize14.0ms (0.3%)

rewrite45.0ms (0.9%)

series393.0ms (7.9%)

simplify90.0ms (1.8%)

prune126.0ms (2.5%)

regimes637.0ms (12.8%)

bsearch66.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (37.2%)

Profiling