Details

analyze618.0ms (13.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	210
1	45	210
0	4	4
1	4	4

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)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (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

25.7b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.8b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite17.0ms (0.4%)

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×	`flip3-+_binary64_1104` `associate-/l_binary64_1046` `flip-+_binary64_1075` `associate-/r_binary64_1045`
2×	`pow1_binary64_1162` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 42

Calls

2 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 x.re y.re) (.f64 x.im y.im))

series132.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

92.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
40.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5449	1541

prune71.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Error

25.0b

Counts

49 → 9

Compiler

Compiled 1312 to 536 computations (59.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
13.8b	(/.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))))
27.7b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.7b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1101`
30×	`sqrt-prod_binary64_1117`
25×	`add-sqr-sqrt_binary64_1123`
24×	`times-frac_binary64_1107`
23×	`add-cube-cbrt_binary64_1136`
12×	`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`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`associate-/l*_binary64_1046`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

4 → 96

Calls

4 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))))
10.0ms	(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	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series196.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(/.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))))
35.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify81.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5305	3217

prune179.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	105	12	117

Error

23.5b

Counts

117 → 12

Compiler

Compiled 4018 to 2409 computations (40% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.6b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.8b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
24.9b	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1101`
32×	`times-frac_binary64_1107`
30×	`add-sqr-sqrt_binary64_1123`
23×	`add-cube-cbrt_binary64_1136`
21×	`associate-r_binary64_1041`
16×	`add-exp-log_binary64_1139`
14×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
10×	`add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162`
5×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/r*_binary64_1045`
4×	`prod-exp_binary64_1150` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`associate-/l_binary64_1046` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
1×	`inv-pow_binary64_1186` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `associate-r/_binary64_1043` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `pow-flip_binary64_1175` `un-div-inv_binary64_1099`

Counts

3 → 100

Calls

3 calls:

19.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
10.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series159.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

98.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
38.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5502	2622

prune127.0ms (2.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	109	12	121

Error

23.5b

Counts

121 → 12

Compiler

Compiled 2769 to 1545 computations (44.2% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

20.1b	(/.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)))))
28.6b	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
28.6b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.6b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite50.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_1133`
17×	`*-un-lft-identity_binary64_1101`
13×	`cbrt-prod_binary64_1132`
10×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
9×	`add-sqr-sqrt_binary64_1123` `add-exp-log_binary64_1139` `add-cube-cbrt_binary64_1136`
8×	`associate-/r/_binary64_1047`
7×	`add-cbrt-cube_binary64_1137`
4×	`unpow-prod-down_binary64_1180` `frac-times_binary64_1111` `add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `pow1_binary64_1162`
3×	`pow1/3_binary64_1183` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
2×	`associate-/l/_binary64_1048` `associate-r/_binary64_1043` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-l/_binary64_1044`
1×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045`

Counts

4 → 74

Calls

4 calls:

22.0ms	(/.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)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
3.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series581.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(/.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)))))
77.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
76.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
75.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5168	2653

prune148.0ms (3.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	85	13	98

Error

22.6b

Counts

98 → 13

Compiler

Compiled 3598 to 1881 computations (47.7% saved)

regimes379.0ms (8.4%)

Accuracy

Total 2.6b remaining (10.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4649 to 3487 computations (25% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	132
1	47	132

end0.0ms (0%)

sample1.4s (31%)

Algorithm

1×

intervals

Results

338.0ms	8000×	body	128	valid
20.0ms	440×	body	128	invalid

Compiler

Compiled 998 to 731 computations (26.8% saved)

Details

analyze618.0ms (13.7%)

sample20.0ms (0.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite17.0ms (0.4%)

series132.0ms (2.9%)

simplify65.0ms (1.4%)

prune71.0ms (1.6%)

localize14.0ms (0.3%)

rewrite46.0ms (1%)

series196.0ms (4.3%)

simplify81.0ms (1.8%)

prune179.0ms (4%)

localize12.0ms (0.3%)

rewrite42.0ms (0.9%)

series159.0ms (3.5%)

simplify78.0ms (1.7%)

prune127.0ms (2.8%)

localize18.0ms (0.4%)

rewrite50.0ms (1.1%)

series581.0ms (12.8%)

simplify63.0ms (1.4%)

prune148.0ms (3.3%)

regimes379.0ms (8.4%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (31%)

Profiling