Details

analyze799.0ms (6.3%)

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)

sample60.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	196×	body	128	valid
10.0ms	18×	body	4096	valid
7.0ms	15×	body	2048	valid
4.0ms	12×	body	1024	valid
3.0ms	11×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune5.0ms (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

40.5b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_3890`
6×	`*-un-lft-identity_binary64_3829`
5×	`add-log-exp_binary64_3868` `add-sqr-sqrt_binary64_3851`
4×	`sqrt-prod_binary64_3845` `add-cube-cbrt_binary64_3864` `sqrt-div_binary64_3846`
3×	`flip3-+_binary64_3832` `add-exp-log_binary64_3867` `flip-+_binary64_3803` `add-cbrt-cube_binary64_3865` `sqrt-pow1_binary64_3847`
2×	`pow1/2_binary64_3909` `associate-*r/_binary64_3771`
1×	`pow-prod-down_binary64_3900` `rem-sqrt-square_binary64_3842` `sum-log_binary64_3920` `distribute-lft-out_binary64_3780` `+-commutative_binary64_3759`

Counts

3 → 40

Calls

3 calls:

17.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
14.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series574.0ms (4.5%)

Counts

3 → 45

Calls

3 calls:

237.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
208.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
129.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1144 to 1029 computations (10.1% saved)

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5166	1396

prune198.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	9	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	9	86

Error

7.3b

Counts

86 → 9

Compiler

Compiled 1665 to 875 computations (47.4% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.3b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
32.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.6b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3851`
10×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829` `cbrt-prod_binary64_3860`
9×	`associate-r_binary64_3769`
8×	`sqrt-prod_binary64_3845`
6×	`add-log-exp_binary64_3868` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `pow1_binary64_3890` `cbrt-div_binary64_3861`
4×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
3×	`unswap-sqr_binary64_3797` `associate-l_binary64_3770`
2×	`pow1/3_binary64_3911` `sqrt-div_binary64_3846` `associate-*r/_binary64_3771`
1×	`pow-prod-down_binary64_3900` `sum-log_binary64_3920` `prod-exp_binary64_3878` `+-commutative_binary64_3759` `*-commutative_binary64_3760` `cbrt-unprod_binary64_3862`

Counts

4 → 65

Calls

4 calls:

19.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
17.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
8.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series1.1s (8.9%)

Counts

4 → 38

Calls

4 calls:

345.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
339.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
226.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
220.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2236 to 1923 computations (14% saved)

simplify168.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4842	2603
1	4842	2603

prune212.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Error

7.2b

Counts

112 → 10

Compiler

Compiled 3345 to 1085 computations (67.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.6b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite91.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_3851`
50×	`sqrt-prod_binary64_3845`
38×	`*-un-lft-identity_binary64_3829`
36×	`times-frac_binary64_3835`
26×	`add-cube-cbrt_binary64_3864`
12×	`difference-of-squares_binary64_3798`
11×	`pow1_binary64_3890`
9×	`associate-/r*_binary64_3773`
6×	`add-log-exp_binary64_3868` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `distribute-lft-out--_binary64_3781`
4×	`sqrt-div_binary64_3846` `associate-/l*_binary64_3774` `sqrt-pow1_binary64_3847`
3×	`pow-prod-down_binary64_3900` `cancel-sign-sub-inv_binary64_3795`
2×	`flip--_binary64_3804` `flip3--_binary64_3833` `associate-/r/_binary64_3775` `pow1/2_binary64_3909`
1×	`flip3-+_binary64_3832` `div-inv_binary64_3826` `div-exp_binary64_3880` `rem-sqrt-square_binary64_3842` `flip-+_binary64_3803` `clear-num_binary64_3828` `sqrt-undiv_binary64_3850` `cbrt-undiv_binary64_3863` `frac-2neg_binary64_3840` `sub-neg_binary64_3822` `diff-log_binary64_3921`

Counts

4 → 108

Calls

4 calls:

30.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
17.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series681.0ms (5.3%)

Counts

4 → 47

Calls

4 calls:

242.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
205.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
173.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
60.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1471 to 1239 computations (15.8% saved)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5007	4122

prune323.0ms (2.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	152	13	165

Error

2.7b

Counts

165 → 13

Compiler

Compiled 4405 to 1748 computations (60.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
31.5b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite158.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_3845`
143×	`add-sqr-sqrt_binary64_3851`
112×	`times-frac_binary64_3835`
100×	`*-un-lft-identity_binary64_3829`
72×	`add-cube-cbrt_binary64_3864`
60×	`associate-r_binary64_3769`
28×	`difference-of-squares_binary64_3798`
14×	`distribute-lft-out--_binary64_3781`
11×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
9×	`associate-/r*_binary64_3773`
7×	`pow1_binary64_3890`
6×	`add-log-exp_binary64_3868` `sqrt-div_binary64_3846` `associate-/l*_binary64_3774`
5×	`unswap-sqr_binary64_3797`
4×	`associate-/r/_binary64_3775`
3×	`cancel-sign-sub-inv_binary64_3795` `flip--_binary64_3804` `flip3--_binary64_3833` `associate-l_binary64_3770`
2×	`div-inv_binary64_3826` `div-exp_binary64_3880` `prod-exp_binary64_3878` `cbrt-undiv_binary64_3863` `cbrt-unprod_binary64_3862`
1×	`flip3-+_binary64_3832` `pow-prod-down_binary64_3900` `rem-sqrt-square_binary64_3842` `flip-+_binary64_3803` `clear-num_binary64_3828` `pow1/2_binary64_3909` `sqrt-undiv_binary64_3850` `associate-r/_binary64_3771` `-commutative_binary64_3760` `frac-2neg_binary64_3840` `sqrt-pow1_binary64_3847` `sub-neg_binary64_3822` `diff-log_binary64_3921`

Counts

4 → 198

Calls

4 calls:

52.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
25.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
17.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series758.0ms (6%)

Counts

4 → 49

Calls

4 calls:

242.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
204.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
176.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
134.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))

Compiler

Compiled 1603 to 1392 computations (13.2% saved)

simplify244.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4925	6809
1	4925	6809

prune744.0ms (5.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	4	6	10
Picked	1	0	1
Done	0	2	2
Total	249	11	260

Error

0.2b

Counts

260 → 11

Compiler

Compiled 7092 to 2589 computations (63.5% saved)

regimes2.2s (17.5%)

Accuracy

Total 18.6b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7240 to 5219 computations (27.9% saved)

bsearch285.0ms (2.2%)

Steps

Iters	Range		Point
8	4.286407987532083e+132	3.279505887650902e+135	2.1953640621976277e+133
9	1.0138572926245806e+76	5.931366564092284e+82	1.9125016493451565e+77
7	1.2803414373194781e+56	5.01602044395433e+57	4.4320159922082814e+57
7	5.6608134726576786e-120	1.9064275874068678e-118	5.722481989834968e-120
7	-4.580493023499429e-282	-2.9164178337707815e-284	-3.906232603684439e-284
5	-9.582129251551642e-223	-3.943021946792792e-223	-7.56364108284337e-223
8	-1.4183595098352533e-157	-6.730041994356548e-162	-6.855362663148291e-162
5	-2.6253015006725035e+119	-8.305496435021174e+118	-2.423886782901208e+119

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	147	251
1	147	251

end0.0ms (0%)

sample3.6s (27.9%)

Algorithm

1×

intervals

Results

560.0ms	6063×	body	128	valid
282.0ms	505×	body	4096	valid
281.0ms	645×	body	2048	valid
159.0ms	435×	body	1024	valid
59.0ms	225×	body	512	valid
22.0ms	127×	body	256	valid

Compiler

Compiled 1182 to 832 computations (29.6% saved)

Details

analyze799.0ms (6.3%)

sample60.0ms (0.5%)

simplify13.0ms (0.1%)

prune5.0ms (0%)

localize20.0ms (0.2%)

rewrite45.0ms (0.4%)

series574.0ms (4.5%)

simplify122.0ms (1%)

prune198.0ms (1.6%)

localize27.0ms (0.2%)

rewrite66.0ms (0.5%)

series1.1s (8.9%)

simplify168.0ms (1.3%)

prune212.0ms (1.7%)

localize24.0ms (0.2%)

rewrite91.0ms (0.7%)

series681.0ms (5.3%)

simplify164.0ms (1.3%)

prune323.0ms (2.5%)

localize28.0ms (0.2%)

rewrite158.0ms (1.2%)

series758.0ms (6%)

simplify244.0ms (1.9%)

prune744.0ms (5.8%)

regimes2.2s (17.5%)

bsearch285.0ms (2.2%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.6s (27.9%)

Profiling