Details

analyze1.5s

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
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample114.0ms

Algorithm

intervals

Results

43.0ms	75×	body	1024	invalid
28.0ms	239×	body	128	valid
9.0ms	25×	body	512	invalid
6.0ms	9×	body	1024	valid
3.0ms	13×	body	256	invalid
3.0ms	8×	body	512	valid
3.0ms	23×	body	128	invalid

simplify230.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5114	72

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 34.2b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.1b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
10.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
9.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
366.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify99.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4809	1251
1	4809	1251

prune108.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 19.7b

Counts

70 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 65

Calls

4 calls:

4.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
5.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
155.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
52.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5055	1650

prune93.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 4.1b

Counts

84 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.2b	(*.f64 (log.f64 x.re) y.re)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`associate-r_binary64`
3×	`exp-prod_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `log-pow_binary64` `exp-diff_binary64` `exp-sum_binary64` `flip--_binary64`

Counts

4 → 62

Calls

4 calls:

5.0ms	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
4.0ms	(*.f64 (log.f64 x.re) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series439.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
153.0ms	(-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
75.0ms	(*.f64 (log.f64 x.re) y.re)
49.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify43.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4975	1246
1	4975	1246

prune59.0ms

Filtered

49 candidates to 74 candidates (-51.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	73	11	84

Merged error: 4.1b

Counts

84 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

86×	`unpow-prod-down_binary64`
84×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
56×	`cbrt-prod_binary64`
50×	`cube-prod_binary64`
14×	`sqr-pow_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`pow-exp_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`pow-to-exp_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3))
2.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
9.0ms	(pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series667.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3))
55.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
376.0ms	(pow.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) 3)
45.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify90.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5853	5679

prune81.0ms

Filtered

85 candidates to 178 candidates (-109.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	178	11	189

Merged error: 4.1b

Counts

189 → 11

regimes270.0ms

Accuracy

54.8% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 20.2b

bsearch281.0ms

Steps

Iters	Range		Point
9	0.00042500248613970435	749013.3338547338	0.9295754959825187
7	6.374146200742313e-68	1.4142309392632907e-65	1.608969993350805e-67
8	1.1293182776367433e-301	1.6236012099480889e-298	2.7192715241158423e-299
7	-1.078183270068929e-220	-3.138841206542437e-222	-7.886014516012344e-222

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	192
1	106	192

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2476×	body	1024	invalid
838.0ms	7590×	body	128	valid
364.0ms	995×	body	512	invalid
94.0ms	409×	body	256	invalid
91.0ms	160×	body	1024	valid
69.0ms	564×	body	128	invalid
53.0ms	144×	body	512	valid
44.0ms	49×	body	2048	invalid
22.0ms	93×	body	256	valid
13.0ms	13×	body	2048	valid

Details

analyze1.5s

sample114.0ms

simplify230.0ms

prune9.0ms

localize24.0ms

rewrite35.0ms

series502.0ms

simplify99.0ms

prune108.0ms

localize15.0ms

rewrite24.0ms

series495.0ms

simplify79.0ms

prune93.0ms

localize11.0ms

rewrite21.0ms

series439.0ms

simplify43.0ms

prune59.0ms

localize12.0ms

rewrite46.0ms

series667.0ms

simplify90.0ms

prune81.0ms

regimes270.0ms

bsearch281.0ms

simplify5.0ms

end0.0ms

sample3.4s

Profiling