Details

analyze825.0ms (13%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify138.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune4.0ms (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: 25.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize26.0ms (0.4%)

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))
24.6b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
7×	`add-log-exp_binary64_1140`
5×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`pow1_binary64_1162` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`sum-log_binary64_1192` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `+-commutative_binary64_1031`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

3 → 53

Calls

3 calls:

17.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
8.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
7.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series198.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

105.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
55.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
37.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5573	1768

prune117.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Merged error: 24.4b

Counts

63 → 6

Compiler

Compiled 1535 to 623 computations (59.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.6b	(/.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))))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.4b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms (0.7%)

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`
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 → 94

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))))
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))

series292.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.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))
34.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune175.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Merged error: 22.4b

Counts

112 → 10

Compiler

Compiled 3670 to 1551 computations (57.7% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.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)))))
14.6b	(/.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))))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite140.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64_1101`
101×	`add-sqr-sqrt_binary64_1123`
94×	`times-frac_binary64_1107`
71×	`sqrt-prod_binary64_1117`
53×	`add-cube-cbrt_binary64_1136`
30×	`associate-r_binary64_1041` `associate-l_binary64_1042`
28×	`add-exp-log_binary64_1139`
24×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
18×	`add-cbrt-cube_binary64_1137`
15×	`unswap-sqr_binary64_1069`
10×	`sqrt-div_binary64_1118`
9×	`div-exp_binary64_1152`
8×	`prod-exp_binary64_1150` `pow1_binary64_1162` `associate-/r*_binary64_1045`
6×	`flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
5×	`cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
2×	`1-exp_binary64_1145` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-/l/_binary64_1048` `rec-exp_binary64_1151` `pow1/2_binary64_1181`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044`

Counts

4 → 184

Calls

4 calls:

57.0ms	(.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)))))
27.0ms	(/.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))))
14.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
13.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series428.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(.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)))))
159.0ms	(/.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))))
48.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify221.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4973	7451
1	4973	7451

prune529.0ms (8.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	196	10	206

Merged error: 22.4b

Counts

206 → 10

Compiler

Compiled 6945 to 4028 computations (42% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.6b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
24.3b	(.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))))

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_1101`
32×	`times-frac_binary64_1107`
31×	`add-sqr-sqrt_binary64_1123`
24×	`add-cube-cbrt_binary64_1136`
21×	`associate-r_binary64_1041`
17×	`add-exp-log_binary64_1139`
16×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
11×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
6×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
5×	`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` `sum-log_binary64_1192` `div-inv_binary64_1098` `rec-exp_binary64_1151` `+-commutative_binary64_1031` `cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
1×	`inv-pow_binary64_1186` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `pow-flip_binary64_1175` `un-div-inv_binary64_1099`

Counts

4 → 113

Calls

4 calls:

34.0ms	(.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))))
11.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
9.0ms	(/.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))

series224.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.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))))
42.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
38.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
36.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4945	2873
1	4945	2873

prune188.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	125	10	135

Merged error: 22.4b

Counts

135 → 10

Compiler

Compiled 2867 to 1538 computations (46.4% saved)

regimes496.0ms (7.8%)

Compiler: Compiled 4094 to 2977 computations (27.3% saved)

bsearch2.0ms (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	32	103
1	32	103

end0.0ms (0%)

sample1.8s (27.9%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
32.0ms	453×	body	128	invalid

Compiler

Compiled 871 to 617 computations (29.2% saved)

Details

analyze825.0ms (13%)

sample37.0ms (0.6%)

simplify138.0ms (2.2%)

prune4.0ms (0.1%)

localize26.0ms (0.4%)

rewrite41.0ms (0.7%)

series198.0ms (3.1%)

simplify93.0ms (1.5%)

prune117.0ms (1.9%)

localize20.0ms (0.3%)

rewrite41.0ms (0.7%)

series292.0ms (4.6%)

simplify63.0ms (1%)

prune175.0ms (2.8%)

localize26.0ms (0.4%)

rewrite140.0ms (2.2%)

series428.0ms (6.8%)

simplify221.0ms (3.5%)

prune529.0ms (8.3%)

localize24.0ms (0.4%)

rewrite72.0ms (1.1%)

series224.0ms (3.5%)

simplify141.0ms (2.2%)

prune188.0ms (3%)

regimes496.0ms (7.8%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (27.9%)

Profiling