Details

analyze626.0ms (6.4%)

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)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

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

26.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite86.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

25.8b

Rules

11×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
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×	`associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `sum-log_binary64_1192` `+-commutative_binary64_1031`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

3 → 53

Calls

3 calls:

8.0ms	(/.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))

Compiler

Compiled 1469 to 193 computations (86.9% saved)

series597.0ms (6.1%)

Error

5.4b

Counts

3 → 63

Calls

3 calls:

324.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
140.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
92.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2202 to 1389 computations (36.9% saved)

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4952	2693
1	4952	2693

prune111.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	8	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

5.3b

Counts

117 → 8

Compiler

Compiled 2308 to 857 computations (62.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
15.8b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
31.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite161.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`associate-/l*_binary64_1046`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 94

Calls

4 calls:

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

Compiler

Compiled 3563 to 1385 computations (61.1% saved)

series911.0ms (9.3%)

Error

5.3b

Counts

4 → 99

Calls

4 calls:

411.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
148.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
135.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
122.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 6144 to 3854 computations (37.3% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5053	5106

prune237.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	192	9	201

Error

5.3b

Counts

201 → 9

Compiler

Compiled 5944 to 2438 computations (59% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
15.8b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite214.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`associate-/l*_binary64_1046`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (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)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))

Compiler

Compiled 3813 to 2242 computations (41.2% saved)

series925.0ms (9.5%)

Error

5.3b

Counts

4 → 99

Calls

4 calls:

384.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
151.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
136.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
125.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6594 to 4984 computations (24.4% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4970	5136
1	4970	5136

prune324.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	195	9	204

Error

5.3b

Counts

204 → 9

Compiler

Compiled 6363 to 3819 computations (40% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

16.3b	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
16.3b	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
16.3b	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
16.6b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))) (/.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite224.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

48×	`*-un-lft-identity_binary64_1101`
36×	`associate-r_binary64_1041`
32×	`times-frac_binary64_1107`
30×	`cbrt-div_binary64_1133`
29×	`add-sqr-sqrt_binary64_1123`
25×	`cbrt-prod_binary64_1132`
24×	`add-cube-cbrt_binary64_1136`
16×	`add-exp-log_binary64_1139` `flip3-+_binary64_1104` `frac-times_binary64_1111` `flip-+_binary64_1075`
12×	`associate-*l/_binary64_1044` `unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
10×	`add-cbrt-cube_binary64_1137`
9×	`pow1_binary64_1162`
6×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
5×	`associate-*r/_binary64_1043`
4×	`add-log-exp_binary64_1140`
3×	`pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `pow1/3_binary64_1183`
2×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r/_binary64_1047`
1×	`associate-l_binary64_1042` `div-inv_binary64_1098` `*-commutative_binary64_1032`

Counts

4 → 114

Calls

4 calls:

32.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))) (/.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
4.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
3.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
3.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))

Compiler

Compiled 5954 to 1464 computations (75.4% saved)

series1.6s (16.2%)

Error

5.3b

Counts

4 → 105

Calls

4 calls:

369.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
357.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
350.0ms	(cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
346.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))) (/.f64 (cbrt.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

Compiler

Compiled 11652 to 7046 computations (39.5% saved)

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4980	9268
1	4980	9268

prune311.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	219	9	228

Error

5.3b

Counts

228 → 9

Compiler

Compiled 9052 to 3228 computations (64.3% saved)

regimes1.1s (11.6%)

Accuracy

Total 10.8b remaining (68.4%)

Threshold costs 0b (0%)

Compiler

Compiled 8749 to 5068 computations (42.1% saved)

bsearch64.0ms (0.7%)

Steps

Iters	Range		Point
6	2.736929534990076e-21	2.474825810031804e-20	2.440833307462582e-20
7	1.6546745656068793e-101	9.019239232029186e-100	1.6871257722081152e-101
6	-7.475488624529926e-106	-9.416075687221754e-107	-1.3781986218689126e-106
5	-1.3485052114971215e+83	-5.946603568596305e+82	-1.3266583380699222e+83

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	170
1	51	170

end0.0ms (0%)

sample1.8s (18.1%)

Algorithm

1×

intervals

Results

334.0ms	8000×	body	128	valid
22.0ms	478×	body	128	invalid

Compiler

Compiled 1814 to 1057 computations (41.7% saved)

Details

analyze626.0ms (6.4%)

sample22.0ms (0.2%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite86.0ms (0.9%)

series597.0ms (6.1%)

simplify82.0ms (0.8%)

prune111.0ms (1.1%)

localize17.0ms (0.2%)

rewrite161.0ms (1.7%)

series911.0ms (9.3%)

simplify91.0ms (0.9%)

prune237.0ms (2.4%)

localize14.0ms (0.1%)

rewrite214.0ms (2.2%)

series925.0ms (9.5%)

simplify93.0ms (1%)

prune324.0ms (3.3%)

localize16.0ms (0.2%)

rewrite224.0ms (2.3%)

series1.6s (16.2%)

simplify133.0ms (1.4%)

prune311.0ms (3.2%)

regimes1.1s (11.6%)

bsearch64.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.8s (18.1%)

Profiling