Details

analyze442.0ms (3.5%)

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)

sample47.0ms (0.4%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
3.0ms	37×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify198.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5740	19

prune7.0ms (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

31.5b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
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))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_410`
22×	`log-pow_binary64_493`
21×	`pow1_binary64_465`
17×	`add-sqr-sqrt_binary64_426`
16×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
6×	`pow1/2_binary64_484` `sqrt-pow1_binary64_422` `associate-/l*_binary64_349`
5×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `add-log-exp_binary64_443`
4×	`associate-/r*_binary64_348` `sqrt-div_binary64_421`
3×	`flip3-+_binary64_407` `flip-+_binary64_378` `sqrt-prod_binary64_420`
2×	`log-div_binary64_491` `div-sub_binary64_409`
1×	`div-exp_binary64_455` `frac-2neg_binary64_415` `div-inv_binary64_401` `sum-log_binary64_495` `clear-num_binary64_403` `cbrt-undiv_binary64_438` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

3 → 74

Calls

6 calls:

11.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))
0.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))

series603.0ms (4.8%)

Counts

3 → 45

Calls

3 calls:

384.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
129.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
90.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1088 to 992 computations (8.8% saved)

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5227	2398

prune162.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	14	119
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Error

0.7b

Counts

121 → 15

Compiler

Compiled 2285 to 622 computations (72.8% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
0.3b	(/.f64 1 (log.f64 base))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1 (log.f64 base))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_426`
26×	`times-frac_binary64_410`
24×	`*-un-lft-identity_binary64_404`
23×	`add-cube-cbrt_binary64_439`
17×	`pow1_binary64_465` `add-exp-log_binary64_442`
16×	`associate-r_binary64_344`
11×	`add-cbrt-cube_binary64_440`
10×	`log-pow_binary64_493`
6×	`associate-l_binary64_345` `add-log-exp_binary64_443`
4×	`div-exp_binary64_455` `associate-/r*_binary64_348` `prod-exp_binary64_453`
3×	`unswap-sqr_binary64_372` `associate-/l*_binary64_349` `sqrt-prod_binary64_420`
2×	`1-exp_binary64_448` `pow1/2_binary64_484` `sqrt-pow1_binary64_422` `div-inv_binary64_401` `sqrt-div_binary64_421` `flip3-+_binary64_407` `rec-exp_binary64_454` `flip-+_binary64_378` `cbrt-undiv_binary64_438` `cbrt-unprod_binary64_437`
1×	`pow-prod-down_binary64_475` `pow-flip_binary64_478` `-commutative_binary64_335` `frac-2neg_binary64_415` `sum-log_binary64_495` `associate-r/_binary64_346` `un-div-inv_binary64_402` `clear-num_binary64_403` `inv-pow_binary64_489` `+-commutative_binary64_334` `rem-sqrt-square_binary64_417`

Counts

4 → 103

Calls

8 calls:

11.0ms	(.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))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series701.0ms (5.6%)

Counts

4 → 48

Calls

4 calls:

392.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
128.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
93.0ms	(+.f64 (.f64 re re) (.f64 im im))
87.0ms	(/.f64 1 (log.f64 base))

Compiler

Compiled 1270 to 1162 computations (8.5% saved)

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5525	2347

prune136.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	146	20	166

Error

0.6b

Counts

166 → 20

Compiler

Compiled 2935 to 1022 computations (65.2% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

30.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.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)))))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
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))))
30.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite232.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_410`
72×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439` `add-sqr-sqrt_binary64_426`
47×	`pow1_binary64_465`
43×	`log-pow_binary64_493`
24×	`associate-/r*_binary64_348`
12×	`add-exp-log_binary64_442`
11×	`add-cbrt-cube_binary64_440`
7×	`associate-/l*_binary64_349`
6×	`div-inv_binary64_401` `add-log-exp_binary64_443`
4×	`div-exp_binary64_455` `cbrt-undiv_binary64_438`
3×	`log-prod_binary64_490`
2×	`log-div_binary64_491` `frac-2neg_binary64_415` `flip3-+_binary64_407` `clear-num_binary64_403` `flip-+_binary64_378`
1×	`rem-log-exp_binary64_445` `sum-log_binary64_495` `associate-/r/_binary64_350` `+-commutative_binary64_334`

Counts

4 → 159

Calls

8 calls:

199.0ms	(+.f64 (.f64 re re) (.f64 im im))
7.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.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))))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series1.3s (10.3%)

Counts

4 → 58

Calls

4 calls:

694.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
390.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
101.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
97.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2282 to 1998 computations (12.4% saved)

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5424	6038

prune221.0ms (1.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	8	11	19
Picked	1	0	1
Done	0	0	0
Total	218	19	237

Error

0.6b

Counts

237 → 19

Compiler

Compiled 5029 to 1486 computations (70.5% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.0b	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
30.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_404`
24×	`times-frac_binary64_410` `add-cube-cbrt_binary64_439` `add-sqr-sqrt_binary64_426`
18×	`log-prod_binary64_490`
17×	`pow1_binary64_465`
15×	`cbrt-prod_binary64_435`
13×	`log-pow_binary64_493`
12×	`associate-+l+_binary64_337` `distribute-rgt-out_binary64_357`
6×	`associate-+r+_binary64_336` `add-cbrt-cube_binary64_440` `associate-/r*_binary64_348` `distribute-lft-in_binary64_353` `add-exp-log_binary64_442` `distribute-lft1-in_binary64_359` `distribute-rgt-in_binary64_354` `cbrt-div_binary64_436`
5×	`flip3-+_binary64_407` `add-log-exp_binary64_443` `flip-+_binary64_378`
4×	`associate-/l*_binary64_349`
2×	`log-div_binary64_491` `associate-/r/_binary64_350` `associate-+r-_binary64_338` `pow1/3_binary64_486`
1×	`div-exp_binary64_455` `frac-2neg_binary64_415` `div-inv_binary64_401` `sum-log_binary64_495` `clear-num_binary64_403` `cbrt-undiv_binary64_438` `+-commutative_binary64_334`

Counts

4 → 108

Calls

8 calls:

14.0ms	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.0ms	(/.f64 (log.f64 base) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
6.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series1.7s (13.9%)

Counts

4 → 55

Calls

4 calls:

1.2s	(/.f64 (log.f64 base) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
209.0ms	(+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
169.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
166.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3180 to 2764 computations (13.1% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4914	3872
1	4914	3872

prune163.0ms (1.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	163	19	182

Error

0.6b

Counts

182 → 19

Compiler

Compiled 4473 to 1413 computations (68.4% saved)

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	370	1546
1	370	1546

regimes828.0ms (6.6%)

Accuracy

Total 17.3b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 3902 to 2966 computations (24% saved)

bsearch168.0ms (1.3%)

Steps

Iters	Range		Point
6	9.144514636146147e+73	1.2700883643188006e+75	8.063615423237896e+74
6	-1.1696442860152739e-272	-1.0591460472724144e-273	-1.3320567237358959e-273
5	-1.0354081137974045e-244	-2.8438584484835733e-245	-6.390324954697034e-245
8	-1.6863291978924692e+125	-1.463160532494197e+121	-1.1582045779288604e+124

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	121
1	93	121

end0.0ms (0%)

sample5.0s (40.1%)

Algorithm

1×

intervals

Results

824.0ms	8000×	body	128	valid
97.0ms	995×	body	128	nan

Compiler

Compiled 3104 to 2323 computations (25.2% saved)

Pareto

0.017944913101717908

Details

analyze442.0ms (3.5%)

sample47.0ms (0.4%)

simplify198.0ms (1.6%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite26.0ms (0.2%)

series603.0ms (4.8%)

simplify89.0ms (0.7%)

prune162.0ms (1.3%)

localize12.0ms (0.1%)

rewrite31.0ms (0.3%)

series701.0ms (5.6%)

simplify86.0ms (0.7%)

prune136.0ms (1.1%)

localize11.0ms (0.1%)

rewrite232.0ms (1.9%)

series1.3s (10.3%)

simplify109.0ms (0.9%)

prune221.0ms (1.8%)

localize16.0ms (0.1%)

rewrite46.0ms (0.4%)

series1.7s (13.9%)

simplify93.0ms (0.7%)

prune163.0ms (1.3%)

simplify28.0ms (0.2%)

regimes828.0ms (6.6%)

bsearch168.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.0s (40.1%)

Profiling