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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample129.0ms

Algorithm

intervals

Results

49.0ms	80×	body	1024	invalid
28.0ms	240×	body	128	valid
12.0ms	30×	body	512	invalid
6.0ms	5×	body	2048	invalid
4.0ms	6×	body	1024	valid
2.0ms	9×	body	256	invalid
2.0ms	13×	body	128	invalid
1.0ms	4×	body	512	valid
1.0ms	5×	body	256	valid
1.0ms	1×	body	2048	valid

simplify227.0ms

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: 35.8b

Counts

2 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.8b	(sin.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)))

rewrite29.0ms

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sin.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)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
41.0ms	(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)))
381.0ms	(sin.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)))

simplify96.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4839	1270
1	4839	1270

prune113.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 20.0b

Counts

70 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
9.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series1.1s

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
342.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
357.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
357.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify72.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5043	1579

prune175.0ms

Filtered

49 candidates to 51 candidates (-4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	51	8	59

Merged error: 20.0b

Counts

59 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.8b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite25.0ms

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
41.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
354.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

simplify98.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4839	1270
1	4839	1270

prune97.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 20.0b

Counts

76 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.9b	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
31.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series407.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
52.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
266.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (neg.f64 x.re)) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
46.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify131.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4817	1147
1	4817	1147

prune67.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	69	10	79

Merged error: 12.6b

Counts

79 → 10

regimes289.0ms

Accuracy

74.2% (5.3b remaining)

Error of 18.3b against oracle of 13.0b and baseline of 33.7b

bsearch275.0ms

Steps

Iters	Range	Point
9	-6.4029118862510934e-307	2.4605920762302808e-304	1.3275016262014e-310
9	-9.529228441581026e-175	-1.1457646468242203e-181	-6.458569401730105e-177
9	-4.1944512240501255e-93	-7.371479824041035e-102	-2.0011844963223532e-93

Iters

Range

Point

-6.4029118862510934e-307

2.4605920762302808e-304

1.3275016262014e-310

-9.529228441581026e-175

-1.1457646468242203e-181

-6.458569401730105e-177

-4.1944512240501255e-93

-7.371479824041035e-102

-2.0011844963223532e-93

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	257
1	97	257

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2505×	body	1024	invalid
869.0ms	7558×	body	128	valid
358.0ms	927×	body	512	invalid
224.0ms	187×	body	2048	invalid
111.0ms	191×	body	1024	valid
86.0ms	359×	body	256	invalid
63.0ms	533×	body	128	invalid
52.0ms	139×	body	512	valid
25.0ms	105×	body	256	valid
7.0ms	7×	body	2048	valid

Details

analyze1.5s

sample129.0ms

simplify227.0ms

prune9.0ms

localize30.0ms

rewrite29.0ms

series511.0ms

simplify96.0ms

prune113.0ms

localize36.0ms

rewrite36.0ms

series1.1s

simplify72.0ms

prune175.0ms

localize24.0ms

rewrite25.0ms

series485.0ms

simplify98.0ms

prune97.0ms

localize23.0ms

rewrite23.0ms

series407.0ms

simplify131.0ms

prune67.0ms

regimes289.0ms

bsearch275.0ms

simplify7.0ms

end0.0ms

sample3.7s

Profiling