Details

analyze561.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune3.0ms (0%)

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

28.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize14.0ms (0.1%)

Local error

Found 6 expressions with local error:

28.4b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
28.4b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
9×	`times-frac_binary64_1076`
7×	`add-log-exp_binary64_1109`
5×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108`
4×	`flip-+_binary64_1044` `flip3-+_binary64_1073`
3×	`associate-/r_binary64_1014` `pow1_binary64_1131` `associate-/l_binary64_1015`
2×	`associate-/r/_binary64_1016` `associate-/l/_binary64_1017` `+-commutative_binary64_1000` `sum-log_binary64_1161`
1×	`frac-2neg_binary64_1081` `cbrt-undiv_binary64_1104` `clear-num_binary64_1069` `div-exp_binary64_1121` `div-inv_binary64_1067`

Counts

3 → 53

Calls

6 calls:

9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series557.0ms (4.8%)

Counts

3 → 63

Calls

3 calls:

331.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
138.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
88.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 1383 to 1146 computations (17.1% saved)

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4955	2693
1	4955	2693

prune210.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	9	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

6.1b

Counts

117 → 9

Compiler

Compiled 2328 to 867 computations (62.8% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.1b	(/.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
18.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
33.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
33.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1070`
28×	`sqrt-prod_binary64_1086`
25×	`add-sqr-sqrt_binary64_1092`
24×	`times-frac_binary64_1076`
23×	`add-cube-cbrt_binary64_1105`
10×	`distribute-lft-out_binary64_1021` `unpow-prod-down_binary64_1149`
8×	`associate-/r*_binary64_1014`
6×	`sqrt-div_binary64_1087` `add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-log-exp_binary64_1109` `pow1_binary64_1131`
5×	`flip-+_binary64_1044` `flip3-+_binary64_1073`
3×	`associate-/l*_binary64_1015`
2×	`associate-/r/_binary64_1016` `pow1/2_binary64_1150` `associate-/l/_binary64_1017` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088`
1×	`frac-2neg_binary64_1081` `cbrt-undiv_binary64_1104` `clear-num_binary64_1069` `+-commutative_binary64_1000` `div-exp_binary64_1121` `sum-log_binary64_1161` `div-inv_binary64_1067`

Counts

4 → 94

Calls

8 calls:

14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

series840.0ms (7.2%)

Counts

4 → 94

Calls

4 calls:

418.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
156.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
136.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
129.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3540 to 2760 computations (22% saved)

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4979	4856
1	4979	4856

prune227.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	188	9	197

Error

6.1b

Counts

197 → 9

Compiler

Compiled 5736 to 2343 computations (59.2% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
18.9b	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
18.9b	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
33.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
33.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1070`
10×	`sqrt-prod_binary64_1086` `add-sqr-sqrt_binary64_1092`
8×	`add-cube-cbrt_binary64_1105`
6×	`pow1_binary64_1131` `cbrt-prod_binary64_1101`
4×	`sqrt-div_binary64_1087` `add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `flip-+_binary64_1044` `distribute-lft-out_binary64_1021` `unpow-prod-down_binary64_1149` `add-log-exp_binary64_1109` `cbrt-div_binary64_1102` `flip3-+_binary64_1073`
2×	`pow1/2_binary64_1150` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088` `pow1/3_binary64_1152`

Counts

4 → 60

Calls

8 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
0.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

series1.1s (9.7%)

Counts

4 → 94

Calls

4 calls:

433.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
424.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
142.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
138.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 8188 to 5416 computations (33.9% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5002	4156

prune318.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	154	9	163

Error

6.1b

Counts

163 → 9

Compiler

Compiled 8133 to 3463 computations (57.4% saved)

localize23.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (cbrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im))))
0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
25.6b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
34.7b	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
34.7b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
34.7b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_1102`
17×	`*-un-lft-identity_binary64_1070`
13×	`cbrt-prod_binary64_1101`
10×	`flip-+_binary64_1044` `flip3-+_binary64_1073`
9×	`add-exp-log_binary64_1108` `add-sqr-sqrt_binary64_1092` `add-cube-cbrt_binary64_1105`
8×	`associate-/r/_binary64_1016`
7×	`add-cbrt-cube_binary64_1106`
4×	`frac-times_binary64_1080` `distribute-lft-out_binary64_1021` `unpow-prod-down_binary64_1149` `add-log-exp_binary64_1109` `pow1_binary64_1131`
3×	`times-frac_binary64_1076` `associate-/l*_binary64_1015` `pow1/3_binary64_1152`
2×	`cbrt-undiv_binary64_1104` `associate-l/_binary64_1013` `associate-/l/_binary64_1017` `associate-r/_binary64_1012` `div-exp_binary64_1121`
1×	`frac-2neg_binary64_1081` `cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `clear-num_binary64_1069` `associate-/r*_binary64_1014` `div-inv_binary64_1067`

Counts

4 → 74

Calls

8 calls:

23.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

series1.7s (14.6%)

Counts

4 → 78

Calls

4 calls:

956.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
251.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
251.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
246.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4299 to 3528 computations (17.9% saved)

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5418	4825

prune292.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	152	9	161

Error

6.1b

Counts

161 → 9

Compiler

Compiled 6214 to 3375 computations (45.7% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	330	1943
1	330	1943

regimes917.0ms (7.9%)

Accuracy

Total 10.4b remaining (68%)

Threshold costs 0b (0%)

Compiler

Compiled 5211 to 3752 computations (28% saved)

bsearch125.0ms (1.1%)

Steps

Iters	Range		Point
6	3.0079263460503392e+141	2.9088058847187696e+142	1.4163550870851477e+142
8	3.351979612061897e-129	7.771908528663381e-126	1.9690354844540234e-126
7	-5.032597015020011e-90	-1.1218585152763866e-91	-9.83945259871375e-91
2	-3276.227314365947	-2968.9548182272824	-3084.182004279282
9	-1.4378203688264434e+28	-2.179227465769176e+22	-2.2148262768226444e+22
7	-4.794225511072451e+135	-5.807041215597531e+133	-4.7218745403061054e+135
9	-6.0645011590064754e+150	-1.2420786890435458e+143	-1.266447775026859e+143

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	269
1	58	269

end0.0ms (0%)

sample4.0s (34.4%)

Algorithm

1×

intervals

Results

366.0ms	8000×	body	128	valid
20.0ms	456×	body	128	invalid

Compiler

Compiled 3379 to 2362 computations (30.1% saved)

Pareto

0.04652694166013866

Details

analyze561.0ms (4.8%)

sample22.0ms (0.2%)

simplify96.0ms (0.8%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite21.0ms (0.2%)

series557.0ms (4.8%)

simplify119.0ms (1%)

prune210.0ms (1.8%)

localize17.0ms (0.1%)

rewrite41.0ms (0.4%)

series840.0ms (7.2%)

simplify93.0ms (0.8%)

prune227.0ms (1.9%)

localize21.0ms (0.2%)

rewrite32.0ms (0.3%)

series1.1s (9.7%)

simplify87.0ms (0.7%)

prune318.0ms (2.7%)

localize23.0ms (0.2%)

rewrite52.0ms (0.4%)

series1.7s (14.6%)

simplify93.0ms (0.8%)

prune292.0ms (2.5%)

simplify26.0ms (0.2%)

regimes917.0ms (7.9%)

bsearch125.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (34.4%)

Profiling