Details

analyze95.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

sample14.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	8	12
1	8	12

prune2.0ms

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

Merged error: 30.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
28.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+.f64 (.f64 re re) (.f64 im im))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4911	443
1	4911	443

prune24.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 7.8b

Counts

33 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
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)))))
28.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
54×	`add-sqr-sqrt_binary64`
38×	`sqrt-pow1_binary64`
32×	`sqrt-div_binary64`
31×	`pow1_binary64`
20×	`*-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-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
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)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
29.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5252	2415

prune67.0ms

Filtered

76 candidates to 146 candidates (-92.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Merged error: 7.8b

Counts

152 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
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)))))
29.4b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.4b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64` `cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
8×	`cbrt-div_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
9.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
122.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
77.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
86.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify116.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4890	2012
1	4890	2012

prune66.0ms

Filtered

74 candidates to 86 candidates (-16.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	86	6	92

Merged error: 7.8b

Counts

92 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.3b	(.f64 (fabs.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
29.4b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.6b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`cbrt-prod_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64`
6×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `prod-exp_binary64` `pow-exp_binary64` `unpow1/3_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
9.0ms	(.f64 (fabs.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

series386.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
136.0ms	(.f64 (fabs.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
79.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
81.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) 1/3)

simplify80.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4933	2007
1	4933	2007

prune71.0ms

Filtered

73 candidates to 91 candidates (-24.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	91	6	97

Merged error: 7.8b

Counts

97 → 6

regimes184.0ms

Accuracy

59.8% (9.5b remaining)

Error of 17.0b against oracle of 7.5b and baseline of 31.2b

bsearch17.0ms

Steps

Iters	Range		Point
6	8.521989101507277e+84	5.101668833587091e+85	4.916291951209594e+85
6	-2.4208140884967115e+154	-3.509476629162686e+153	-6.47123416696789e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

end0.0ms

sample362.0ms

Algorithm

intervals

Results

236.0ms

8000×

body

valid

Details

analyze95.0ms

sample14.0ms

simplify12.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series47.0ms

simplify100.0ms

prune24.0ms

localize9.0ms

rewrite36.0ms

series147.0ms

simplify88.0ms

prune67.0ms

localize9.0ms

rewrite24.0ms

series360.0ms

simplify116.0ms

prune66.0ms

localize17.0ms

rewrite25.0ms

series386.0ms

simplify80.0ms

prune71.0ms

regimes184.0ms

bsearch17.0ms

simplify3.0ms

end0.0ms

sample362.0ms

Profiling