Details

sample336.0ms

Algorithm

intervals

Results

213.0ms	57×	body	640	valid
49.0ms	71×	body	1280	valid
26.0ms	252×	body	80	valid
9.0ms	28×	body	320	valid
2.0ms	11×	body	160	valid

simplify284.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune21.0ms

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: 31.9b

Counts

2 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(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.im)
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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune126.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 17.6b

Counts

70 → 5

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)
1.0b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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)))

series78.0ms

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)))
25.0ms	(* (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)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	299	557
1	864	497
2	2274	481
3	5002	479

prune132.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 3.1b

Counts

86 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (* -1 x.re)) y.re)
1.0b	(* (atan2 x.im x.re) y.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`exp-prod` `pow-prod-down`
2×	`exp-sum` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `exp-diff` `diff-log`

Counts

3 → 53

Calls

3 calls:

7.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (* -1 x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series40.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms	(* (log (* -1 x.re)) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify62.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	224	328
1	723	286
2	3027	278
3	5002	278

prune120.0ms

Filtered

62 candidates to 41 candidates (33.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	62	9	71

Merged error: 3.1b

Counts

71 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
0.6b	(cbrt y.im)
1.0b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt y.im)
1.0ms	(cbrt y.im)
1.0ms	(cbrt y.im)
6.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt y.im)
21.0ms	(cbrt y.im)
22.0ms	(cbrt y.im)
28.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

simplify172.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (168.0ms)

Iter	Nodes	Cost
0	175	316
1	431	278
2	1248	234
3	4677	221
4	5001	215

prune90.0ms

Filtered

64 candidates to 49 candidates (23.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 3.1b

Counts

73 → 9

regimes453.0ms

Accuracy

61.7% (6.4b remaining)

Error of 9.1b against oracle of 2.7b and baseline of 19.3b

bsearch310.0ms

Steps

Iters	Range		Point
7	376735214628221.2	2.487198078455393e+16	4071253643875412.0
8	-2.9265542436951078e-261	-9.539819824638375e-266	-3.3536859738233693e-264
9	-5.204985700414936e-141	-3.0579871170688905e-146	-4.2798434174935106e-144
8	-1.486399975514783e-10	-5.880082306549498e-15	-8.764566283937148e-11

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	54
1	62	54
2	62	54

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2024×	body	1280	valid
850.0ms	8076×	body	80	valid
668.0ms	1436×	body	640	valid
213.0ms	654×	body	320	valid
63.0ms	294×	body	160	valid

Details

sample336.0ms

simplify284.0ms

prune21.0ms

localize34.0ms

rewrite21.0ms

series91.0ms

simplify81.0ms

prune126.0ms

localize16.0ms

rewrite18.0ms

series78.0ms

simplify59.0ms

prune132.0ms

localize12.0ms

rewrite16.0ms

series40.0ms

simplify62.0ms

prune120.0ms

localize16.0ms

rewrite11.0ms

series92.0ms

simplify172.0ms

prune90.0ms

regimes453.0ms

bsearch310.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling