Details

analyze529.0ms (10.9%)

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 (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify162.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (0.1%)

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

Merged error: 23.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.1b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1109` `*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
9×	`times-frac_binary64_1094`
7×	`add-log-exp_binary64_1124`
5×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
4×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
3×	`associate-/r_binary64_1034` `pow1_binary64_1146` `associate-/l_binary64_1035`
2×	`associate-/l/_binary64_1037` `sum-log_binary64_1176` `associate-/r/_binary64_1036` `+-commutative_binary64_1020`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

3 → 53

Calls

3 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))

series293.0ms (6%)

Counts

3 → 9

Calls

3 calls:

180.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
75.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
38.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5214	1768

prune95.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 22.7b

Counts

63 → 8

Compiler

Compiled 1577 to 653 computations (58.6% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.9b	(/.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))))
27.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.2b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1088`
28×	`sqrt-prod_binary64_1103`
25×	`add-sqr-sqrt_binary64_1109`
24×	`times-frac_binary64_1094`
23×	`add-cube-cbrt_binary64_1120`
10×	`unpow-prod-down_binary64_1164` `distribute-lft-out_binary64_1041`
8×	`associate-/r*_binary64_1034`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `sqrt-div_binary64_1104` `add-log-exp_binary64_1124` `pow1_binary64_1146`
5×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
3×	`associate-/l*_binary64_1035`
2×	`rem-sqrt-square_binary64_1101` `associate-/l/_binary64_1037` `associate-/r/_binary64_1036` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 94

Calls

4 calls:

18.0ms	(/.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))

series422.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(/.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))))
78.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
48.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5447	3187

prune151.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	104	10	114

Merged error: 20.2b

Counts

114 → 10

Compiler

Compiled 3658 to 1547 computations (57.7% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
16.0b	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
27.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.2b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_1088`
36×	`add-sqr-sqrt_binary64_1109`
30×	`associate-r_binary64_1030`
28×	`times-frac_binary64_1094`
25×	`sqrt-prod_binary64_1103`
22×	`add-cube-cbrt_binary64_1120`
13×	`add-exp-log_binary64_1123`
9×	`add-cbrt-cube_binary64_1121`
8×	`unpow-prod-down_binary64_1164` `pow1_binary64_1146` `distribute-lft-out_binary64_1041`
6×	`sqrt-div_binary64_1104` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
5×	`unswap-sqr_binary64_1056`
4×	`prod-exp_binary64_1134`
3×	`associate-l_binary64_1031`
2×	`rem-sqrt-square_binary64_1101` `associate-*l/_binary64_1033` `cbrt-unprod_binary64_1118` `frac-times_binary64_1098` `associate-/r/_binary64_1036` `div-exp_binary64_1136` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`-commutative_binary64_1021` `rec-exp_binary64_1135` `sum-log_binary64_1176` `un-div-inv_binary64_1086` `1-exp_binary64_1129` `+-commutative_binary64_1020` `cbrt-undiv_binary64_1119` `pow-prod-down_binary64_1156` `associate-r/_binary64_1032` `div-inv_binary64_1085`

Counts

4 → 102

Calls

4 calls:

24.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (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))

series395.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
68.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
47.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5273	2904

prune160.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	114	10	124

Merged error: 20.2b

Counts

124 → 10

Compiler

Compiled 3955 to 1859 computations (53% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
15.9b	(/.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))))
27.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite109.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64_1088`
101×	`add-sqr-sqrt_binary64_1109`
94×	`times-frac_binary64_1094`
71×	`sqrt-prod_binary64_1103`
53×	`add-cube-cbrt_binary64_1120`
30×	`associate-r_binary64_1030` `associate-l_binary64_1031`
28×	`add-exp-log_binary64_1123`
24×	`unpow-prod-down_binary64_1164` `distribute-lft-out_binary64_1041`
18×	`add-cbrt-cube_binary64_1121`
15×	`unswap-sqr_binary64_1056`
10×	`sqrt-div_binary64_1104`
9×	`div-exp_binary64_1136`
8×	`associate-/r*_binary64_1034` `prod-exp_binary64_1134` `pow1_binary64_1146`
6×	`associate-/r/_binary64_1036` `flip-+_binary64_1062` `flip3-+_binary64_1091`
5×	`cbrt-undiv_binary64_1119`
4×	`cbrt-unprod_binary64_1118` `add-log-exp_binary64_1124`
3×	`associate-/l*_binary64_1035` `div-inv_binary64_1085`
2×	`rem-sqrt-square_binary64_1101` `associate-/l/_binary64_1037` `rec-exp_binary64_1135` `1-exp_binary64_1129` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `associate-l/_binary64_1033` `frac-times_binary64_1098` `pow-prod-down_binary64_1156` `associate-*r/_binary64_1032`

Counts

4 → 184

Calls

4 calls:

49.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
15.0ms	(/.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))))
9.0ms	(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)))

series618.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
249.0ms	(/.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))))
53.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
49.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify131.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4964	7451
1	4964	7451

prune348.0ms (7.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	194	12	206

Merged error: 20.2b

Counts

206 → 12

Compiler

Compiled 6787 to 3899 computations (42.6% saved)

regimes142.0ms (2.9%)

Compiler: Compiled 1149 to 1022 computations (11.1% saved)

bsearch1.0ms (0%)

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	37	107
1	37	107

end0.0ms (0%)

sample884.0ms (18.2%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	128	valid
22.0ms	481×	body	128	invalid

Compiler

Compiled 286 to 236 computations (17.5% saved)

Details

analyze529.0ms (10.9%)

sample21.0ms (0.4%)

simplify162.0ms (3.3%)

prune2.0ms (0.1%)

localize13.0ms (0.3%)

rewrite22.0ms (0.5%)

series293.0ms (6%)

simplify51.0ms (1.1%)

prune95.0ms (2%)

localize19.0ms (0.4%)

rewrite46.0ms (0.9%)

series422.0ms (8.7%)

simplify82.0ms (1.7%)

prune151.0ms (3.1%)

localize23.0ms (0.5%)

rewrite53.0ms (1.1%)

series395.0ms (8.1%)

simplify78.0ms (1.6%)

prune160.0ms (3.3%)

localize15.0ms (0.3%)

rewrite109.0ms (2.2%)

series618.0ms (12.7%)

simplify131.0ms (2.7%)

prune348.0ms (7.2%)

regimes142.0ms (2.9%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample884.0ms (18.2%)

Profiling