Details

analyze323.0ms

Algorithm

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

sample35.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
7.0ms	26×	body	2560	valid
6.0ms	15×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 38.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2.0 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.2b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 40

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2.0 (+.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)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt.f64 (.f64 2.0 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4936	551
1	4936	551

prune82.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 17.8b

Counts

50 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.7b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
16.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune95.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 17.8b

Counts

143 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

8.2b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

25.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 4) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5058	634

prune85.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 17.8b

Counts

75 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2.0)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.4b	(sqrt.f64 (.f64 (.f64 im im) 2.0))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`sqrt-pow1_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 105

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2.0)) (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)
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2.0))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2.0)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (.f64 (.f64 im im) 2.0))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4917	2308
1	4917	2308

prune96.0ms

Filtered

81 candidates to 117 candidates (-44.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	1	3	4
Picked	1	0	1
Done	2	0	2
Total	116	8	124

Merged error: 10.2b

Counts

124 → 8

regimes256.0ms

Accuracy

47.7% (14.0b remaining)

Error of 24.5b against oracle of 10.5b and baseline of 37.3b

bsearch121.0ms

Steps

Iters	Range		Point
10	7.879054437551379e+57	1.2371522206970305e+70	8.99727301172237e+57
6	9.624781449627483e+56	7.879054437551379e+57	9.810431200447886e+56
7	1.2694555867180504e-78	2.4744285905050064e-77	1.4310037079643518e-78
6	1.6748916741442751e-118	1.4878500325911111e-117	4.000710555951358e-118
9	3.254534619998204e-188	7.142653857917004e-181	3.3363403467192465e-186
8	-3.0721949970216363e-267	-2.615506481311857e-271	-3.2410829879680627e-270
9	-1.8388342581148795e+169	-2.6092957248578346e+162	-2.649308197943826e+162

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	130
1	77	130

end0.0ms

sample898.0ms

Algorithm

intervals

Results

292.0ms	6048×	body	80	valid
180.0ms	664×	body	2560	valid
115.0ms	523×	body	1280	valid
87.0ms	262×	body	5120	valid
47.0ms	274×	body	640	valid
23.0ms	147×	body	320	valid
7.0ms	82×	body	160	valid

Details

analyze323.0ms

sample35.0ms

simplify5.0ms

prune5.0ms

localize10.0ms

rewrite22.0ms

series50.0ms

simplify55.0ms

prune82.0ms

localize14.0ms

rewrite48.0ms

series33.0ms

simplify72.0ms

prune95.0ms

localize21.0ms

rewrite40.0ms

series33.0ms

simplify64.0ms

prune85.0ms

localize12.0ms

rewrite39.0ms

series51.0ms

simplify46.0ms

prune96.0ms

regimes256.0ms

bsearch121.0ms

simplify3.0ms

end0.0ms

sample898.0ms

Profiling