Details

analyze331.0ms

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

sample33.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
5.0ms	19×	body	2560	valid
5.0ms	15×	body	5120	valid
5.0ms	20×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms

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: 36.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.7b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
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)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (.f64 re re) (.f64 im im))
113.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
31.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4937	1040
1	4937	1040

prune81.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 15.2b

Counts

64 → 6

localize13.0ms

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)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.5b	(sqrt.f64 (.f64 (.f64 im im) 2))
28.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms

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)) (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))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
33.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5289	3612

prune105.0ms

Filtered

81 candidates to 117 candidates (-44.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Merged error: 9.0b

Counts

123 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(*.f64 (fabs.f64 im) (sqrt.f64 2))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64` `times-frac_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `difference-of-squares_binary64`
4×	`sqrt-div_binary64`
3×	`associate-l_binary64` `distribute-lft-out--_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

15.0ms	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
5.0ms	(*.f64 (fabs.f64 im) (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)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
20.0ms	(*.f64 (fabs.f64 im) (sqrt.f64 2))
31.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4986	2127
1	4986	2127

prune84.0ms

Filtered

63 candidates to 98 candidates (-55.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	99	9	108

Merged error: 5.4b

Counts

108 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.3b	(.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
10.0ms	(.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (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)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 (.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
26.0ms	(.f64 (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
32.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4963	2325
1	4963	2325

prune89.0ms

Filtered

67 candidates to 102 candidates (-52.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 5.4b

Counts

111 → 8

regimes138.0ms

Accuracy

56.4% (13.1b remaining)

Error of 20.6b against oracle of 7.5b and baseline of 37.6b

bsearch75.0ms

Steps

Iters	Range		Point
7	1.2822796960487663e-74	2.77425001376497e-72	1.81655221984481e-74
7	8.86272932155161e-88	3.504196007464333e-86	2.6578910116797832e-86
5	3.7433371288569895e-103	1.3436823564083405e-102	6.975022293022832e-103
7	-3.829287484042333e+66	-2.946386029196321e+64	-2.0754615002920678e+66

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	69	125
1	69	125

end0.0ms

sample918.0ms

Algorithm

intervals

Results

291.0ms	6009×	body	80	valid
189.0ms	673×	body	2560	valid
122.0ms	526×	body	1280	valid
90.0ms	269×	body	5120	valid
51.0ms	276×	body	640	valid
24.0ms	164×	body	320	valid
8.0ms	83×	body	160	valid

Details

analyze331.0ms

sample33.0ms

simplify15.0ms

prune3.0ms

localize11.0ms

rewrite26.0ms

series191.0ms

simplify80.0ms

prune81.0ms

localize13.0ms

rewrite35.0ms

series172.0ms

simplify106.0ms

prune105.0ms

localize14.0ms

rewrite35.0ms

series183.0ms

simplify73.0ms

prune84.0ms

localize19.0ms

rewrite43.0ms

series205.0ms

simplify82.0ms

prune89.0ms

regimes138.0ms

bsearch75.0ms

simplify5.0ms

end0.0ms

sample918.0ms

Profiling