Details

analyze465.0ms (2.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample35.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms	20×	body	4096	valid
8.0ms	187×	body	128	valid
4.0ms	20×	body	2048	valid
4.0ms	22×	body	1024	valid
1.0ms	5×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

36.5b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite132.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

36.4b

Rules

8×	`pow1_binary64_4231` `add-log-exp_binary64_4209`
7×	`*-un-lft-identity_binary64_4170`
6×	`add-sqr-sqrt_binary64_4192`
5×	`add-cube-cbrt_binary64_4205`
4×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `flip3-+_binary64_4173` `sqrt-div_binary64_4187` `flip-+_binary64_4144` `sqrt-prod_binary64_4186`
3×	`sqrt-pow1_binary64_4188`
2×	`pow1/2_binary64_4250` `sum-log_binary64_4261` `+-commutative_binary64_4100` `associate-*r/_binary64_4112`
1×	`rem-sqrt-square_binary64_4183` `distribute-lft-out_binary64_4121` `pow-prod-down_binary64_4241`

Counts

4 → 51

Calls

4 calls:

8.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1235 to 435 computations (64.8% saved)

series537.0ms (3%)

Error

5.8b

Counts

4 → 51

Calls

4 calls:

138.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
121.0ms	(+.f64 (.f64 re re) (.f64 im im))
118.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
111.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 1656 to 1462 computations (11.7% saved)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4941	1562
1	4941	1562

prune116.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Error

5.6b

Counts

103 → 6

Compiler

Compiled 1471 to 756 computations (48.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.6b	(sqrt.f64 (.f64 2 (.f64 im im)))

rewrite201.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

51×	`add-sqr-sqrt_binary64_4192`
50×	`sqrt-prod_binary64_4186`
38×	`*-un-lft-identity_binary64_4170`
36×	`times-frac_binary64_4176`
26×	`add-cube-cbrt_binary64_4205`
12×	`difference-of-squares_binary64_4139`
11×	`pow1_binary64_4231`
9×	`associate-/r*_binary64_4114`
6×	`add-log-exp_binary64_4209` `add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `distribute-lft-out--_binary64_4122`
4×	`sqrt-pow1_binary64_4188` `sqrt-div_binary64_4187` `associate-/l*_binary64_4115`
3×	`pow-prod-down_binary64_4241` `cancel-sign-sub-inv_binary64_4136`
2×	`pow1/2_binary64_4250` `flip3--_binary64_4174` `flip--_binary64_4145` `associate-/r/_binary64_4116`
1×	`flip3-+_binary64_4173` `flip-+_binary64_4144` `rem-sqrt-square_binary64_4183` `diff-log_binary64_4262` `sub-neg_binary64_4163` `div-exp_binary64_4221` `cbrt-undiv_binary64_4204` `sqrt-undiv_binary64_4191` `frac-2neg_binary64_4181` `clear-num_binary64_4169` `div-inv_binary64_4167`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2948 to 960 computations (67.4% saved)

series601.0ms (3.4%)

Error

1.4b

Counts

4 → 49

Calls

4 calls:

181.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
169.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
155.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
46.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2169 to 1739 computations (19.8% saved)

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4967	4217
1	4967	4217

prune197.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	152	11	163

Error

1.4b

Counts

163 → 11

Compiler

Compiled 3139 to 1303 computations (58.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
0.5b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite553.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

1.4b

Rules

402×	`times-frac_binary64_4176`
305×	`add-sqr-sqrt_binary64_4192`
275×	`sqrt-prod_binary64_4186`
252×	`*-un-lft-identity_binary64_4170`
200×	`add-cube-cbrt_binary64_4205`
52×	`difference-of-squares_binary64_4139`
34×	`associate-/r*_binary64_4114`
26×	`distribute-lft-out--_binary64_4122`
15×	`associate-/l*_binary64_4115`
11×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
9×	`div-inv_binary64_4167`
6×	`add-log-exp_binary64_4209`
5×	`pow1_binary64_4231`
4×	`sqrt-div_binary64_4187` `div-exp_binary64_4221` `cbrt-undiv_binary64_4204`
3×	`cancel-sign-sub-inv_binary64_4136`
2×	`flip3--_binary64_4174` `flip--_binary64_4145` `frac-2neg_binary64_4181` `clear-num_binary64_4169` `associate-/l/_binary64_4117`
1×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `flip-+_binary64_4144` `rem-sqrt-square_binary64_4183` `diff-log_binary64_4262` `sub-neg_binary64_4163` `associate-/r/_binary64_4116`

Counts

4 → 323

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
15.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 8422 to 2395 computations (71.6% saved)

series768.0ms (4.3%)

Error

0.5b

Counts

4 → 55

Calls

4 calls:

183.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
180.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
177.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
163.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 2629 to 2152 computations (18.1% saved)

simplify161.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5019	15839

prune399.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	375	3	378
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	380	9	389

Error

0.5b

Counts

389 → 9

Compiler

Compiled 6687 to 2150 computations (67.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (sqrt.f64 (fabs.f64 im)))))
0.3b	(*.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite1.3s (7.1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

1168×	`sqrt-prod_binary64_4186`
1008×	`times-frac_binary64_4176`
698×	`add-sqr-sqrt_binary64_4192`
575×	`*-un-lft-identity_binary64_4170`
536×	`associate-r_binary64_4110`
465×	`add-cube-cbrt_binary64_4205`
110×	`difference-of-squares_binary64_4139`
55×	`distribute-lft-out--_binary64_4122`
27×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
14×	`pow1_binary64_4231`
10×	`prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `div-inv_binary64_4167`
7×	`associate-l_binary64_4111`
6×	`add-log-exp_binary64_4209` `pow-prod-down_binary64_4241` `unswap-sqr_binary64_4138` `div-exp_binary64_4221` `cbrt-undiv_binary64_4204`
3×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `cancel-sign-sub-inv_binary64_4136` `sqrt-unprod_binary64_4190`
2×	`sqrt-div_binary64_4187` `*-commutative_binary64_4101` `sqrt-undiv_binary64_4191`
1×	`flip3-+_binary64_4173` `flip-+_binary64_4144` `rem-sqrt-square_binary64_4183` `diff-log_binary64_4262` `flip3--_binary64_4174` `sub-neg_binary64_4163` `flip--_binary64_4145` `associate-*r/_binary64_4112` `associate-/r/_binary64_4116`

Counts

4 → 619

Calls

4 calls:

115.0ms	(.f64 (.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (sqrt.f64 (fabs.f64 im)))))
9.0ms	(*.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 16679 to 6234 computations (62.6% saved)

series675.0ms (3.8%)

Error

0.3b

Counts

4 → 49

Calls

4 calls:

184.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
179.0ms	(.f64 (.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (sqrt.f64 (fabs.f64 im)))))
174.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
74.0ms	(*.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 2991 to 2340 computations (21.8% saved)

simplify264.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

668 → 668

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4977	25689
1	4977	25689

prune548.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	667	1	668
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	667	10	677

Error

0.3b

Counts

677 → 10

Compiler

Compiled 9215 to 3520 computations (61.8% saved)

regimes9.3s (52.2%)

Accuracy

Total 17.5b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 58865 to 43880 computations (25.5% saved)

bsearch158.0ms (0.9%)

Steps

Iters	Range		Point
10	1.0360696323756301e+105	6.377131750768449e+114	2.632424878302857e+113
9	8.193823792025529e-165	7.521736247427974e-160	1.0073950938736855e-164
9	2.077035039325274e-210	9.229829202903851e-202	9.000466420424405e-202
8	1.69806293764723e-262	2.473211920527083e-258	6.993600331950945e-261
5	-2.5264223356322037e+154	-6.999991241821771e+153	-1.3360753823747522e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	176
1	100	176

end5.0ms (0%)

Compiler: Compiled 111 to 76 computations (31.5% saved)

sample1.2s (6.9%)

Algorithm

1×

intervals

Results

281.0ms	6075×	body	128	valid
151.0ms	527×	body	4096	valid
143.0ms	625×	body	2048	valid
70.0ms	402×	body	1024	valid
35.0ms	240×	body	512	valid
14.0ms	131×	body	256	valid

Compiler

Compiled 320 to 255 computations (20.3% saved)

Details

analyze465.0ms (2.6%)

sample35.0ms (0.2%)

simplify7.0ms (0%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite132.0ms (0.7%)

series537.0ms (3%)

simplify73.0ms (0.4%)

prune116.0ms (0.7%)

localize13.0ms (0.1%)

rewrite201.0ms (1.1%)

series601.0ms (3.4%)

simplify59.0ms (0.3%)

prune197.0ms (1.1%)

localize14.0ms (0.1%)

rewrite553.0ms (3.1%)

series768.0ms (4.3%)

simplify161.0ms (0.9%)

prune399.0ms (2.2%)

localize18.0ms (0.1%)

rewrite1.3s (7.1%)

series675.0ms (3.8%)

simplify264.0ms (1.5%)

prune548.0ms (3.1%)

regimes9.3s (52.2%)

bsearch158.0ms (0.9%)

simplify5.0ms (0%)

end5.0ms (0%)

sample1.2s (6.9%)

Profiling