Details

analyze994.0ms (7.6%)

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	20×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

Error

27.3b

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))
0.3b	(+.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)))

rewrite116.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

27.1b

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:

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))

Compiler

Compiled 1469 to 193 computations (86.9% saved)

series610.0ms (4.7%)

Error

5.0b

Counts

3 → 60

Calls

3 calls:

315.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
150.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
100.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2046 to 1284 computations (37.2% saved)

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5051	2576

prune158.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Error

5.0b

Counts

114 → 9

Compiler

Compiled 2283 to 862 computations (62.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
16.5b	(/.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))))
30.2b	(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)))

rewrite248.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

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:

15.0ms	(/.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))))
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)))
6.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))

Compiler

Compiled 3813 to 2242 computations (41.2% saved)

series1.2s (9.3%)

Error

5.0b

Counts

4 → 92

Calls

4 calls:

496.0ms	(/.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))))
205.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
199.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
176.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6246 to 4750 computations (24% saved)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4973	4801
1	4973	4801

prune372.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	188	9	197

Error

5.0b

Counts

197 → 9

Compiler

Compiled 6099 to 3661 computations (40% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.3b	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
0.8b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))))
26.2b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))

rewrite355.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

140×	`*-un-lft-identity_binary64_1101`
138×	`times-frac_binary64_1107`
72×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
34×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
24×	`associate-/r*_binary64_1045`
17×	`add-exp-log_binary64_1139`
11×	`add-cbrt-cube_binary64_1137` `associate-/r/_binary64_1047`
8×	`div-exp_binary64_1152` `add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/l*_binary64_1046`
6×	`div-inv_binary64_1098`
5×	`pow1_binary64_1162`
4×	`cbrt-undiv_binary64_1135`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `1-exp_binary64_1145` `rec-exp_binary64_1151` `sum-log_binary64_1192` `+-commutative_binary64_1031`
1×	`inv-pow_binary64_1186` `pow-flip_binary64_1175`

Counts

4 → 171

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))))
15.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
15.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
8.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))

Compiler

Compiled 5627 to 2756 computations (51% saved)

series1.1s (8.7%)

Error

5.0b

Counts

4 → 93

Calls

4 calls:

443.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
344.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re))))
154.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
112.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

Compiler

Compiled 4704 to 3460 computations (26.4% saved)

simplify178.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5074	9327

prune413.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	262	11	273

Error

2.6b

Counts

273 → 11

Compiler

Compiled 6728 to 3280 computations (51.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.8b	(cbrt.f64 (/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.7b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.7b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.7b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite518.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

103×	`*-un-lft-identity_binary64_1101`
60×	`times-frac_binary64_1107`
43×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
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×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/3_binary64_1183` `cbrt-div_binary64_1133`

Counts

4 → 147

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
14.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
14.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
12.0ms	(cbrt.f64 (/.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 9513 to 4428 computations (53.5% saved)

series1.9s (14.9%)

Error

2.6b

Counts

4 → 97

Calls

4 calls:

538.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
396.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
392.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
373.0ms	(/.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 13304 to 8124 computations (38.9% saved)

simplify151.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5629	8940

prune870.0ms (6.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	244	11	255

Error

2.6b

Counts

255 → 11

Compiler

Compiled 13942 to 6566 computations (52.9% saved)

regimes1.3s (10%)

Accuracy

Total 11.4b remaining (79.8%)

Threshold costs 0b (0%)

Compiler

Compiled 6809 to 4218 computations (38.1% saved)

bsearch118.0ms (0.9%)

Steps

Iters	Range		Point
9	5.261012177257102e+79	9.232655022452831e+86	1.315316451044619e+86
6	1.4455124447971334e-123	7.993289479926725e-123	2.1472644582174967e-123
10	-1.5447351947110331e-100	-1.2451099552022908e-113	-8.849808015292707e-110
8	-4.362551450141799e+80	-1.5989624956840602e+77	-2.7839182926984815e+79

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	44	176
1	44	176

end0.0ms (0%)

sample2.0s (15.6%)

Algorithm

1×

intervals

Results

390.0ms	8000×	body	128	valid
26.0ms	443×	body	128	invalid

Compiler

Compiled 1426 to 869 computations (39.1% saved)

Details

analyze994.0ms (7.6%)

sample22.0ms (0.2%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite116.0ms (0.9%)

series610.0ms (4.7%)

simplify130.0ms (1%)

prune158.0ms (1.2%)

localize21.0ms (0.2%)

rewrite248.0ms (1.9%)

series1.2s (9.3%)

simplify110.0ms (0.8%)

prune372.0ms (2.8%)

localize11.0ms (0.1%)

rewrite355.0ms (2.7%)

series1.1s (8.7%)

simplify178.0ms (1.4%)

prune413.0ms (3.1%)

localize17.0ms (0.1%)

rewrite518.0ms (4%)

series1.9s (14.9%)

simplify151.0ms (1.1%)

prune870.0ms (6.6%)

regimes1.3s (10%)

bsearch118.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.0s (15.6%)

Profiling