Details

analyze516.0ms (7.6%)

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 (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify158.0ms (2.3%)

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

Merged error: 27.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite27.0ms (0.4%)

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:

13.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
5.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series291.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

179.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
70.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
42.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5573	1768

prune92.0ms (1.4%)

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: 26.4b

Counts

63 → 8

Compiler

Compiled 1639 to 673 computations (58.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
16.8b	(/.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))))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.2b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite46.0ms (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:

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))))
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))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series408.0ms (6%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(/.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))))
77.0ms	(+.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)))
43.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune150.0ms (2.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	103	11	114

Merged error: 24.2b

Counts

114 → 11

Compiler

Compiled 3653 to 1530 computations (58.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.9b	(cbrt.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite85.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64_1101`
60×	`times-frac_binary64_1107`
43×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
30×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
21×	`cbrt-prod_binary64_1132`
15×	`associate-/r*_binary64_1045`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`associate-/l*_binary64_1046`
8×	`associate-/r/_binary64_1047`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`associate-/l/_binary64_1048`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `div-inv_binary64_1098`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`pow1/3_binary64_1183` `cbrt-div_binary64_1133`

Counts

4 → 147

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.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)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
12.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series915.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
167.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
166.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
166.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5042	6314

prune409.0ms (6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	159	11	170

Merged error: 24.2b

Counts

170 → 11

Compiler

Compiled 9694 to 4529 computations (53.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3)
0.9b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.5b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3))

rewrite74.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64_1101`
75×	`times-frac_binary64_1107`
74×	`unpow-prod-down_binary64_1180`
52×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
48×	`cbrt-prod_binary64_1132`
42×	`cube-prod_binary64_1129`
32×	`distribute-lft-out_binary64_1052`
10×	`associate-/r/_binary64_1047`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`add-log-exp_binary64_1140`
5×	`pow1_binary64_1162` `div-inv_binary64_1098` `associate-/r*_binary64_1045`
3×	`pow-unpow_binary64_1178` `associate-/l*_binary64_1046`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `associate-/l/_binary64_1048` `cube-div_binary64_1130` `unpow3_binary64_1167` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `sqr-pow_binary64_1073`
1×	`pow1/3_binary64_1183` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170` `cbrt-div_binary64_1133` `rem-cbrt-cube_binary64_1125`

Counts

4 → 170

Calls

4 calls:

17.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3))
16.0ms	(pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3)
15.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series1.2s (17.7%)

Counts

4 → 12

Calls

4 calls:

788.0ms	(pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3)
178.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) 3))
167.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
68.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify124.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6007	7073

prune224.0ms (3.3%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	182	11	193

Merged error: 24.2b

Counts

193 → 11

Compiler

Compiled 4781 to 2391 computations (50% saved)

regimes367.0ms (5.4%)

Compiler: Compiled 4554 to 3297 computations (27.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	48
1	26	48

end0.0ms (0%)

sample1.4s (20%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	128	valid
20.0ms	494×	body	128	invalid

Compiler

Compiled 935 to 676 computations (27.7% saved)

Details

analyze516.0ms (7.6%)

sample22.0ms (0.3%)

simplify158.0ms (2.3%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite27.0ms (0.4%)

series291.0ms (4.3%)

simplify74.0ms (1.1%)

prune92.0ms (1.4%)

localize18.0ms (0.3%)

rewrite46.0ms (0.7%)

series408.0ms (6%)

simplify65.0ms (1%)

prune150.0ms (2.2%)

localize16.0ms (0.2%)

rewrite85.0ms (1.3%)

series915.0ms (13.5%)

simplify104.0ms (1.5%)

prune409.0ms (6%)

localize14.0ms (0.2%)

rewrite74.0ms (1.1%)

series1.2s (17.7%)

simplify124.0ms (1.8%)

prune224.0ms (3.3%)

regimes367.0ms (5.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (20%)

Profiling