Details

analyze490.0ms (2.4%)

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)

sample53.0ms (0.3%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
4.0ms	35×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify280.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	5740	19

prune13.0ms (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

28.8b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize16.0ms (0.1%)

Local error

Found 6 expressions with local error:

26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.4b	(/.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))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_84`
22×	`log-pow_binary64_167`
21×	`pow1_binary64_139`
17×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-pow1_binary64_96` `associate-/l*_binary64_23` `pow1/2_binary64_158`
5×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
4×	`associate-/r*_binary64_22` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `flip3-+_binary64_81`
2×	`log-div_binary64_165` `div-sub_binary64_83`
1×	`+-commutative_binary64_8` `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` `sum-log_binary64_169`

Counts

3 → 74

Calls

6 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)))
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))

series778.0ms (3.8%)

Counts

3 → 45

Calls

3 calls:

494.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
181.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
102.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1088 to 992 computations (8.8% saved)

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5227	2398

prune216.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	12	119
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Error

0.2b

Counts

121 → 13

Compiler

Compiled 2257 to 600 computations (73.4% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

27.8b	(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))))
27.8b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_84`
72×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
47×	`pow1_binary64_139`
43×	`log-pow_binary64_167`
24×	`associate-/r*_binary64_22`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
7×	`associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117` `div-inv_binary64_75`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`log-prod_binary64_164`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `log-div_binary64_165` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `rem-log-exp_binary64_119` `associate-/r/_binary64_24` `sum-log_binary64_169`

Counts

4 → 159

Calls

8 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))))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series1.8s (8.7%)

Counts

4 → 58

Calls

4 calls:

978.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
516.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
146.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
125.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2282 to 1998 computations (12.4% saved)

simplify143.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5387	6021

prune265.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	211	6	217
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	216	14	230

Error

0.2b

Counts

230 → 14

Compiler

Compiled 4978 to 1420 computations (71.5% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.7b	(pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3)
0.6b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
0.6b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3))
0.7b	(pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3)
27.8b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64_139`
17×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`times-frac_binary64_84`
13×	`add-exp-log_binary64_116`
12×	`add-cbrt-cube_binary64_114`
11×	`log-pow_binary64_167`
8×	`cbrt-prod_binary64_109`
4×	`add-log-exp_binary64_117` `associate-/l_binary64_23` `associate-/r_binary64_22` `log-div_binary64_165`
3×	`rem-cube-cbrt_binary64_101` `pow-exp_binary64_146` `log-prod_binary64_164` `pow-unpow_binary64_155`
2×	`cube-mult_binary64_108` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `cube-div_binary64_107` `div-exp_binary64_129` `unpow-prod-down_binary64_157` `flip-+_binary64_52` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-*l/_binary64_21` `div-sub_binary64_83` `unpow3_binary64_144` `cube-prod_binary64_106` `flip3-+_binary64_81`
1×	`cbrt-div_binary64_110` `rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `pow1/3_binary64_160` `frac-2neg_binary64_89` `div-inv_binary64_75` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `clear-num_binary64_77`

Counts

4 → 95

Calls

8 calls:

7.0ms	(pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3)
7.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
5.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
2.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series2.3s (11.3%)

Counts

4 → 55

Calls

4 calls:

1.0s	(pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3)
625.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (log.f64 base)) 1/2) 3))
510.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
153.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2252 to 2034 computations (9.7% saved)

simplify125.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4985	3483
1	4985	3483

prune197.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	149	15	164

Error

0.1b

Counts

164 → 15

Compiler

Compiled 3373 to 1326 computations (60.7% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
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))))
0.6b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3))
0.7b	(pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3)
27.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64_109`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
5×	`cbrt-div_binary64_110`
4×	`add-log-exp_binary64_117`
3×	`rem-cube-cbrt_binary64_101` `pow-exp_binary64_146` `pow1/3_binary64_160` `pow-unpow_binary64_155`
2×	`cube-mult_binary64_108` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `cube-div_binary64_107` `unpow-prod-down_binary64_157` `flip-+_binary64_52` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-*l/_binary64_21` `unpow3_binary64_144` `cube-prod_binary64_106` `flip3-+_binary64_81`
1×	`rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `pow-prod-down_binary64_149`

Counts

4 → 69

Calls

8 calls:

22.0ms	(pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3)
6.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3))
0.0ms	(log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

series2.8s (13.9%)

Counts

4 → 54

Calls

4 calls:

1.4s	(pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3)
907.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (+.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))))) (log.f64 base)) 1/2) 3))
256.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
229.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2962 to 2626 computations (11.3% saved)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5546	2767

prune193.0ms (0.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	120	18	138

Error

0.1b

Counts

138 → 18

Compiler

Compiled 3515 to 1354 computations (61.5% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	393	1793
1	393	1793

regimes1.6s (8.1%)

Accuracy

Total 17.3b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 4526 to 3290 computations (27.3% saved)

bsearch479.0ms (2.4%)

Steps

Iters	Range		Point
7	5.587914849225441e+81	2.628809029749955e+83	1.0066570199945735e+83
8	8.928847658558929e-163	4.0754413199395115e-160	9.790932882769397e-163
7	1.2190831893185469e-231	1.4668707820029931e-229	1.4446922132637966e-229
9	8.624351738361032e-257	7.03774589227268e-251	2.5433593506319202e-253
11	1.6931332341815532e-307	7.733662414909044e-281	5.57434679198083e-283
8	-1.286788467934322e-197	-4.814198199068222e-200	-1.7324615588834855e-199
8	-1.0899080262621188e+60	-2.64474217773024e+57	-2.081558982118848e+59

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	238
1	108	238

end0.0ms (0%)

sample8.1s (39.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
134.0ms	1000×	body	128	nan

Compiler

Compiled 3722 to 2630 computations (29.3% saved)

Pareto

0.04931176422936988

Details

analyze490.0ms (2.4%)

sample53.0ms (0.3%)

simplify280.0ms (1.4%)

prune13.0ms (0.1%)

localize16.0ms (0.1%)

rewrite24.0ms (0.1%)

series778.0ms (3.8%)

simplify85.0ms (0.4%)

prune216.0ms (1.1%)

localize22.0ms (0.1%)

rewrite54.0ms (0.3%)

series1.8s (8.7%)

simplify143.0ms (0.7%)

prune265.0ms (1.3%)

localize15.0ms (0.1%)

rewrite29.0ms (0.1%)

series2.3s (11.3%)

simplify125.0ms (0.6%)

prune197.0ms (1%)

localize19.0ms (0.1%)

rewrite53.0ms (0.3%)

series2.8s (13.9%)

simplify73.0ms (0.4%)

prune193.0ms (0.9%)

simplify33.0ms (0.2%)

regimes1.6s (8.1%)

bsearch479.0ms (2.4%)

simplify6.0ms (0%)

end0.0ms (0%)

sample8.1s (39.9%)

Profiling