Details

analyze546.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	8×	body	80	invalid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune6.0ms

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: 29.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
29.2b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
12.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
33.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5334	951

prune94.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 28.9b

Counts

63 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
19.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
10.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
6.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
43.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5503	1525

prune117.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 24.9b

Counts

105 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im))))
19.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
54×	`sqrt-prod_binary64`
27×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
9×	`associate-/l*_binary64`
8×	`flip3-+_binary64` `div-exp_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`div-inv_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 193

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im))))
32.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	4856
1	4962	4856

prune155.0ms

Filtered

123 candidates to 205 candidates (-66.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	205	11	216

Merged error: 24.9b

Counts

216 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
19.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
18×	`add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64`
10×	`sqrt-div_binary64`
9×	`div-exp_binary64`
8×	`pow1_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

27.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
13.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im)))))
47.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4989	3794
1	4989	3794

prune115.0ms

Filtered

116 candidates to 172 candidates (-48.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	171	12	183

Merged error: 24.9b

Counts

183 → 12

regimes503.0ms

Accuracy

28.4% (2.2b remaining)

Error of 25.4b against oracle of 23.2b and baseline of 26.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	83
1	29	83

end0.0ms

sample597.0ms

Algorithm

intervals

Results

357.0ms	8000×	body	80	valid
22.0ms	496×	body	80	invalid

Details

analyze546.0ms

sample22.0ms

simplify5.0ms

prune6.0ms

localize10.0ms

rewrite19.0ms

series53.0ms

simplify51.0ms

prune94.0ms

localize12.0ms

rewrite27.0ms

series70.0ms

simplify63.0ms

prune117.0ms

localize14.0ms

rewrite41.0ms

series80.0ms

simplify76.0ms

prune155.0ms

localize14.0ms

rewrite55.0ms

series99.0ms

simplify67.0ms

prune115.0ms

regimes503.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample597.0ms

Profiling