Details

analyze520.0ms (12.1%)

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)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify218.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5232	30

prune2.0ms (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

30.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
29.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

2 → 44

Calls

2 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series141.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
41.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6255	1595

prune73.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

29.6b

Counts

51 → 6

Compiler

Compiled 1312 to 510 computations (61.1% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
17.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
32.7b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
32.7b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1101`
28×	`sqrt-prod_binary64_1117`
25×	`add-sqr-sqrt_binary64_1123`
24×	`times-frac_binary64_1107`
23×	`add-cube-cbrt_binary64_1136`
10×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
8×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re 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)))
6.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series225.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
41.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify89.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5542	3247

prune139.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

27.2b

Counts

114 → 7

Compiler

Compiled 3623 to 1482 computations (59.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

18.3b	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
18.3b	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
32.7b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
32.7b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123` `sqrt-prod_binary64_1117`
8×	`add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162` `cbrt-prod_binary64_1132`
4×	`unpow-prod-down_binary64_1180` `add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118` `cbrt-div_binary64_1133`
2×	`rem-sqrt-square_binary64_1114` `pow1/3_binary64_1183` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 60

Calls

4 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.im y.re) (.f64 x.re y.im)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))

series338.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
143.0ms	(cbrt.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4945	1460
1	4945	1460

prune125.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Error

27.2b

Counts

79 → 7

Compiler

Compiled 3607 to 1391 computations (61.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (neg.f64 x.re) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
32.7b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64_1107`
47×	`add-sqr-sqrt_binary64_1123`
46×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
36×	`sqrt-prod_binary64_1117`
21×	`distribute-rgt-neg-in_binary64_1059` `distribute-lft-neg-in_binary64_1058`
10×	`associate-/l*_binary64_1046`
7×	`neg-mul-1_binary64_1097`
6×	`associate-/r*_binary64_1045`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
3×	`pow1_binary64_1162`
2×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `neg-sub0_binary64_1096` `distribute-frac-neg_binary64_1064` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

2 → 107

Calls

2 calls:

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

series85.0ms (2%)

Counts

2 → 6

Calls

2 calls:

61.0ms	(/.f64 (neg.f64 x.re) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
24.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4934	3506
1	4934	3506

prune130.0ms (3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	111	9	120

Error

16.1b

Counts

120 → 9

Compiler

Compiled 2274 to 1424 computations (37.4% saved)

regimes545.0ms (12.7%)

Accuracy

Total 4.6b remaining (25.7%)

Threshold costs 0b (0%)

Compiler

Compiled 3324 to 2487 computations (25.2% saved)

bsearch39.0ms (0.9%)

Steps

Iters	Range		Point
9	4.709958251452121e+64	3.598163599365733e+69	3.54338862761989e+69
7	-1.1438161232924655e+125	-6.786679073780433e+123	-7.462055629753792e+124

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	72
1	69	72

end0.0ms (0%)

sample1.2s (27.9%)

Algorithm

1×

intervals

Results

346.0ms	8000×	body	128	valid
20.0ms	485×	body	128	invalid

Compiler

Compiled 702 to 523 computations (25.5% saved)

Details

analyze520.0ms (12.1%)

sample21.0ms (0.5%)

simplify218.0ms (5.1%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.5%)

series141.0ms (3.3%)

simplify78.0ms (1.8%)

prune73.0ms (1.7%)

localize17.0ms (0.4%)

rewrite43.0ms (1%)

series225.0ms (5.3%)

simplify89.0ms (2.1%)

prune139.0ms (3.3%)

localize18.0ms (0.4%)

rewrite31.0ms (0.7%)

series338.0ms (7.9%)

simplify63.0ms (1.5%)

prune125.0ms (2.9%)

localize8.0ms (0.2%)

rewrite23.0ms (0.5%)

series85.0ms (2%)

simplify80.0ms (1.9%)

prune130.0ms (3%)

regimes545.0ms (12.7%)

bsearch39.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (27.9%)

Profiling