Details

analyze417.0ms (7%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
4.0ms	41×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify193.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5740	19

prune5.0ms (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

Error

33.5b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms (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:

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

series147.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5313	1833

prune95.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Error

7.4b

Counts

85 → 12

Compiler

Compiled 1750 to 439 computations (74.9% saved)

localize11.0ms (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))))
32.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms (0.6%)

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:

7.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series296.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
116.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
33.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5141	4862

prune152.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	169	14	183

Error

7.3b

Counts

183 → 14

Compiler

Compiled 4076 to 1111 computations (72.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (log.f64 base))
0.3b	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
32.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_441`
25×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425` `add-cube-cbrt_binary64_454`
16×	`associate-l_binary64_360`
15×	`pow1_binary64_480`
12×	`add-exp-log_binary64_457`
11×	`add-cbrt-cube_binary64_455`
9×	`log-prod_binary64_505` `log-pow_binary64_508`
6×	`add-log-exp_binary64_458`
4×	`associate-r_binary64_359` `associate-/r*_binary64_363`
3×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393` `log-div_binary64_506` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `rem-log-exp_binary64_460` `sum-log_binary64_510` `-commutative_binary64_350` `frac-2neg_binary64_430` `+-commutative_binary64_349`

Counts

4 → 98

Calls

4 calls:

11.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
6.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(/.f64 1/2 (log.f64 base))

series252.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
93.0ms	(/.f64 1/2 (log.f64 base))
32.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	1931
1	4996	1931

prune103.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	109	15	124

Error

7.3b

Counts

124 → 15

Compiler

Compiled 2235 to 870 computations (61.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
0.5b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3))
0.7b	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3)
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64_425`
94×	`log-pow_binary64_508`
79×	`pow1_binary64_480`
64×	`add-sqr-sqrt_binary64_441`
63×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
62×	`cbrt-prod_binary64_450`
56×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
22×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/l*_binary64_364`
5×	`div-inv_binary64_416`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `associate-/r*_binary64_363`
3×	`pow-unpow_binary64_496` `sqrt-prod_binary64_435`
2×	`flip3-+_binary64_422` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `sqr-pow_binary64_391` `cube-div_binary64_448` `flip-+_binary64_393` `log-div_binary64_506` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`
1×	`clear-num_binary64_418` `pow1/3_binary64_501` `cbrt-div_binary64_451` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `rem-sqrt-square_binary64_432`

Counts

4 → 211

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3))
8.0ms	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3)
8.0ms	(/.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)))

series418.0ms (7%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3)
104.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
97.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) 3))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5632	6151

prune184.0ms (3.1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	220	18	238

Error

7.3b

Counts

238 → 18

Compiler

Compiled 4774 to 1159 computations (75.7% saved)

regimes966.0ms (16.1%)

Accuracy

Total 11.0b remaining (61.4%)

Threshold costs 0b (0%)

Compiler

Compiled 4731 to 3371 computations (28.7% saved)

bsearch167.0ms (2.8%)

Steps

Iters	Range		Point
7	2.6130879275993026e+70	4.00660660214703e+72	3.706762994210151e+72
7	6.284332119691707e-173	9.597343688447874e-171	8.172516521987715e-172
7	-3.7879851419238027e-180	-5.1730444466795143e-182	-1.1819915383869406e-181
8	-7.034482890442465e+104	-2.8789405806716967e+101	-3.4367372751557022e+103

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	52	112
1	52	112

end0.0ms (0%)

sample2.0s (33.9%)

Algorithm

1×

intervals

Results

783.0ms	8000×	body	128	valid
95.0ms	1020×	body	128	nan

Compiler

Compiled 1033 to 724 computations (29.9% saved)

Details

analyze417.0ms (7%)

sample38.0ms (0.6%)

simplify193.0ms (3.2%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series147.0ms (2.5%)

simplify79.0ms (1.3%)

prune95.0ms (1.6%)

localize11.0ms (0.2%)

rewrite35.0ms (0.6%)

series296.0ms (4.9%)

simplify95.0ms (1.6%)

prune152.0ms (2.5%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series252.0ms (4.2%)

simplify51.0ms (0.8%)

prune103.0ms (1.7%)

localize13.0ms (0.2%)

rewrite57.0ms (1%)

series418.0ms (7%)

simplify105.0ms (1.7%)

prune184.0ms (3.1%)

regimes966.0ms (16.1%)

bsearch167.0ms (2.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.0s (33.9%)

Profiling