Details

analyze1.5s

Algorithm: search

sample129.0ms

Algorithm

intervals

Results

39.0ms	53×	body	1280	invalid
28.0ms	245×	body	80	valid
18.0ms	35×	body	640	invalid
8.0ms	22×	body	320	invalid
5.0ms	6×	body	1280	valid
2.0ms	3×	body	320	valid
2.0ms	14×	body	80	invalid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	invalid

simplify382.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune34.0ms

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: 34.3b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	197	426
1	513	389
2	1157	387
3	2556	387
4	5002	387

prune114.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 19.7b

Counts

70 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune121.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 2.9b

Counts

83 → 5

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (log (* -1 x.re)) y.re)
1.2b	(* (atan2 x.im x.re) y.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1`
8×	`associate-l`
6×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `add-cbrt-cube`
3×	`pow-prod-down`
2×	`prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

5.0ms	(* (log (* -1 x.re)) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)

series17.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(* (log (* -1 x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify45.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	155	182
1	566	156
2	2421	155
3	5001	155

prune80.0ms

Filtered

27 candidates to 44 candidates (-63.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	44	5	49

Merged error: 2.9b

Counts

49 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (* (log (* -1 x.re)) y.re))
0.8b	(cbrt (* (log (* -1 x.re)) y.re))
0.8b	(cbrt (* (log (* -1 x.re)) y.re))
1.2b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 45

Calls

4 calls:

4.0ms	(cbrt (* (log (* -1 x.re)) y.re))
4.0ms	(cbrt (* (log (* -1 x.re)) y.re))
4.0ms	(cbrt (* (log (* -1 x.re)) y.re))
3.0ms	(* (atan2 x.im x.re) y.im)

series76.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (* (log (* -1 x.re)) y.re))
22.0ms	(cbrt (* (log (* -1 x.re)) y.re))
23.0ms	(cbrt (* (log (* -1 x.re)) y.re))
6.0ms	(* (atan2 x.im x.re) y.im)

simplify132.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 4 (40.0ms)

Iter	Nodes	Cost
0	143	326
1	372	283
2	805	259
3	1402	253
4	4143	244
5	5001	244

prune145.0ms

Filtered

40 candidates to 57 candidates (-42.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Merged error: 2.9b

Counts

62 → 5

regimes377.0ms

Accuracy

59.7% (6.5b remaining)

Error of 10.2b against oracle of 3.6b and baseline of 19.9b

bsearch3.3s

Steps

Iters	Range		Point
10	-8.352463798467824e-302	8.961118581826923e-306	2.8440857855007e-310
5	-2.0594049404670683e-111	-6.86393256349418e-112	-1.0568496377120418e-111
7	-1246709.381972574	-26948.01860751898	-27302.8460117604

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	55
1	57	55
2	57	55

end0.0ms

analyze1.3s

Algorithm: search

sample3.7s

Algorithm

intervals

Results

1.3s	1849×	body	1280	invalid
832.0ms	7588×	body	80	valid
646.0ms	1323×	body	640	invalid
189.0ms	564×	body	320	invalid
84.0ms	115×	body	1280	valid
80.0ms	161×	body	640	valid
55.0ms	232×	body	160	invalid
44.0ms	390×	body	80	invalid
35.0ms	92×	body	320	valid
10.0ms	44×	body	160	valid

Details

analyze1.5s

sample129.0ms

simplify382.0ms

prune34.0ms

localize24.0ms

rewrite21.0ms

series86.0ms

simplify76.0ms

prune114.0ms

localize16.0ms

rewrite17.0ms

series74.0ms

simplify58.0ms

prune121.0ms

localize12.0ms

rewrite10.0ms

series17.0ms

simplify45.0ms

prune80.0ms

localize19.0ms

rewrite15.0ms

series76.0ms

simplify132.0ms

prune145.0ms

regimes377.0ms

bsearch3.3s

simplify2.0ms

end0.0ms

analyze1.3s

sample3.7s

Profiling