Details

analyze445.0ms (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

30.0ms	256×	body	128	valid
3.0ms	32×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify199.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

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

33.3b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

31.0b	(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))
0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_84`
22×	`log-pow_binary64_167`
20×	`pow1_binary64_139`
16×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-pow1_binary64_96` `associate-/l*_binary64_23` `pow1/2_binary64_158`
4×	`add-cbrt-cube_binary64_114` `associate-/r*_binary64_22` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94`
2×	`add-log-exp_binary64_117` `flip-+_binary64_52` `log-div_binary64_165` `div-sub_binary64_83` `flip3-+_binary64_81`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77`

Counts

2 → 63

Calls

4 calls:

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

series533.0ms (4.2%)

Counts

2 → 36

Calls

2 calls:

407.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
126.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 942 to 829 computations (12% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4948	2319
1	4948	2319

prune158.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	86	13	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	88	13	101

Error

0.5b

Counts

101 → 13

Compiler

Compiled 2017 to 594 computations (70.6% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

32.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.3b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.2b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.2b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.3b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
32.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_84`
71×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
46×	`pow1_binary64_139`
43×	`log-pow_binary64_167`
24×	`associate-/r*_binary64_22`
11×	`add-exp-log_binary64_116`
10×	`add-cbrt-cube_binary64_114`
7×	`associate-/l*_binary64_23`
6×	`div-inv_binary64_75`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`add-log-exp_binary64_117` `log-prod_binary64_164`
2×	`frac-2neg_binary64_89` `log-div_binary64_165` `clear-num_binary64_77`
1×	`flip-+_binary64_52` `rem-log-exp_binary64_119` `associate-/r/_binary64_24` `flip3-+_binary64_81`

Counts

3 → 148

Calls

6 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
5.0ms	(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 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series1.3s (10.1%)

Counts

3 → 56

Calls

3 calls:

691.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
462.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
132.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2242 to 1920 computations (14.4% saved)

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5150	6612

prune232.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	195	9	204
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	203	14	217

Error

0.4b

Counts

217 → 14

Compiler

Compiled 5185 to 1647 computations (68.2% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

32.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.4b	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
0.3b	(/.f64 1/2 (log.f64 base))
0.3b	(/.f64 1/2 (log.f64 base))
0.4b	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
32.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_100`
25×	`times-frac_binary64_84`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`associate-l_binary64_19`
14×	`pow1_binary64_139`
11×	`add-exp-log_binary64_116`
10×	`add-cbrt-cube_binary64_114`
9×	`log-prod_binary64_164` `log-pow_binary64_167`
4×	`associate-r_binary64_18` `associate-/r*_binary64_22`
3×	`distribute-lft-in_binary64_27` `add-log-exp_binary64_117` `distribute-rgt-in_binary64_28` `associate-/l*_binary64_23`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `unswap-sqr_binary64_46` `log-div_binary64_165`
1×	`-commutative_binary64_9` `flip-+_binary64_52` `frac-2neg_binary64_89` `associate-l/_binary64_21` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `clear-num_binary64_77` `flip3-+_binary64_81`

Counts

3 → 87

Calls

6 calls:

11.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(/.f64 1/2 (log.f64 base))
0.0ms	(/.f64 1/2 (log.f64 base))
0.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))

series676.0ms (5.3%)

Counts

3 → 38

Calls

3 calls:

453.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
129.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
94.0ms	(/.f64 1/2 (log.f64 base))

Compiler

Compiled 1076 to 960 computations (10.8% saved)

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4952	2548
1	4952	2548

prune120.0ms (0.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	124	15	139

Error

0.4b

Counts

139 → 15

Compiler

Compiled 2595 to 1033 computations (60.2% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

32.0b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.3b	(/.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))))))
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)))))
0.2b	(/.f64 1/2 (/.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)))))))
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)))))
0.3b	(/.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))))))
32.0b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.0b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_78`
24×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `times-frac_binary64_84`
18×	`log-prod_binary64_164`
17×	`pow1_binary64_139`
15×	`cbrt-prod_binary64_109`
13×	`log-pow_binary64_167`
12×	`distribute-rgt-out_binary64_31` `associate-+l+_binary64_11`
6×	`add-cbrt-cube_binary64_114` `distribute-lft-in_binary64_27` `cbrt-div_binary64_110` `associate-+r+_binary64_10` `distribute-rgt-in_binary64_28` `distribute-lft1-in_binary64_33` `associate-/r*_binary64_22` `add-exp-log_binary64_116`
5×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`associate-/l*_binary64_23`
2×	`associate-+r-_binary64_12` `pow1/3_binary64_160` `log-div_binary64_165` `associate-/r/_binary64_24`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `sum-log_binary64_169`

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))))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(/.f64 1/2 (/.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)))))))

series1.8s (14.3%)

Counts

4 → 61

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))))))
280.0ms	(+.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)))))
170.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
169.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3262 to 2836 computations (13.1% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	4627
1	4966	4627

prune186.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	169	15	184

Error

0.4b

Counts

184 → 15

Compiler

Compiled 4987 to 1707 computations (65.8% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	334	1617
1	334	1617

regimes1.2s (9.3%)

Compiler: Compiled 4086 to 3126 computations (23.5% saved)

bsearch84.0ms (0.7%)

Steps

Iters	Range		Point
6	1.2115297715276313e+82	7.80059377831237e+82	6.398018456610941e+82
7	-1.120041190733667e+66	-1.7704294965337192e+64	-5.775193541606794e+65

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes381.0ms (3%)

Compiler: Compiled 602 to 678 computations (-12.6% saved)

bsearch116.0ms (0.9%)

Steps

Iters	Range		Point
10	1.4389854441249282e+72	1.2115297715276313e+82	3.872290499114305e+79
7	-1.120041190733667e+66	-1.7704294965337192e+64	-1.1003460488858435e+66

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes624.0ms (4.9%)

Compiler: Compiled 498 to 590 computations (-18.5% saved)

bsearch179.0ms (1.4%)

Steps

Iters	Range		Point
4	3.530560780890053e+53	5.547577036334488e+53	3.566774754745039e+53
6	-3.8175462707007656e-267	-5.057926971781147e-268	-3.1529758544172198e-267
10	-1.8271885542848841e-193	-1.1136242590386202e-203	-2.209684678500573e-195
9	-2.22576313674214e-63	-1.3896785023829336e-70	-7.602092955966798e-69

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes332.0ms (2.6%)

Compiler: Compiled 214 to 286 computations (-33.6% saved)

bsearch315.0ms (2.5%)

Steps

Iters	Range		Point
4	3.530560780890053e+53	5.547577036334488e+53	3.566774754745039e+53
8	6.6579627195788e-109	2.039948444011865e-104	2.0817400427423985e-108
5	3.1071390683541995e-156	8.559737245928748e-156	6.260590942950154e-156
10	1.6601534123058575e-267	1.919981057922559e-256	3.2243445988748503e-267
6	-3.8175462707007656e-267	-5.057926971781147e-268	-3.773241576281863e-267
10	-1.8271885542848841e-193	-1.1136242590386202e-203	-6.356426208317572e-194
9	-2.22576313674214e-63	-1.3896785023829336e-70	-6.993069225899243e-67

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes249.0ms (2%)

Compiler: Compiled 86 to 150 computations (-74.4% saved)

bsearch139.0ms (1.1%)

Steps

Iters	Range		Point
4	3.530560780890053e+53	5.547577036334488e+53	3.566774754745039e+53
8	6.6579627195788e-109	2.039948444011865e-104	6.371292140426413e-107
5	3.1071390683541995e-156	8.559737245928748e-156	4.1472290625588017e-156
8	-1.8156337173702916e-95	-1.7470184820244587e-98	-4.747324768854928e-98

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes142.0ms (1.1%)

Compiler: Compiled 62 to 122 computations (-96.8% saved)

bsearch56.0ms (0.4%)

Steps

Iters	Range		Point
2	7.814326988604853e-107	8.817619512771813e-107	7.939738554125723e-107
8	-0.009782177265350476	-1.6591029219226232e-05	-0.009642333378035816

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes46.0ms (0.4%)

Compiler: Compiled 42 to 98 computations (-133.3% saved)

bsearch59.0ms (0.5%)

Steps

Iters	Range		Point
10	-2.2430460060809845e-299	3.089592582666883e-306	5.06454586808178e-309

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.2%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch22.0ms (0.2%)

Steps

Iters	Range		Point
7	42.16250606631296	941.110876634214	42.7275721746072

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes23.0ms (0.2%)

Accuracy

Total 17.5b remaining (98.3%)

Threshold costs 0b (0%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 266 to 175 computations (34.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	129	401
1	129	401

end0.0ms (0%)

sample2.5s (19.3%)

Algorithm

1×

intervals

Results

865.0ms	8000×	body	128	valid
97.0ms	995×	body	128	nan

Compiler

Compiled 1305 to 975 computations (25.3% saved)

Pareto

-0.4494891230881748

Details

analyze445.0ms (3.5%)

sample47.0ms (0.4%)

simplify199.0ms (1.6%)

prune7.0ms (0.1%)

localize15.0ms (0.1%)

rewrite18.0ms (0.1%)

series533.0ms (4.2%)

simplify77.0ms (0.6%)

prune158.0ms (1.2%)

localize12.0ms (0.1%)

rewrite32.0ms (0.3%)

series1.3s (10.1%)

simplify99.0ms (0.8%)

prune232.0ms (1.8%)

localize11.0ms (0.1%)

rewrite26.0ms (0.2%)

series676.0ms (5.3%)

simplify84.0ms (0.7%)

prune120.0ms (0.9%)

localize18.0ms (0.1%)

rewrite43.0ms (0.3%)

series1.8s (14.3%)

simplify100.0ms (0.8%)

prune186.0ms (1.5%)

simplify26.0ms (0.2%)

regimes1.2s (9.3%)

bsearch84.0ms (0.7%)

regimes381.0ms (3%)

bsearch116.0ms (0.9%)

regimes624.0ms (4.9%)

bsearch179.0ms (1.4%)

regimes332.0ms (2.6%)

bsearch315.0ms (2.5%)

regimes249.0ms (2%)

bsearch139.0ms (1.1%)

regimes142.0ms (1.1%)

bsearch56.0ms (0.4%)

regimes46.0ms (0.4%)

bsearch59.0ms (0.5%)

regimes30.0ms (0.2%)

bsearch22.0ms (0.2%)

regimes23.0ms (0.2%)

bsearch12.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.5s (19.3%)

Profiling