Details

sample324.0ms

Algorithm

intervals

Results

190.0ms	23×	body	320	valid
46.0ms	67×	body	1280	valid
29.0ms	257×	body	80	valid
26.0ms	54×	body	640	valid
1.0ms	3×	body	160	valid

simplify38.0ms

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

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.0b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
34.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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

series90.0ms

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)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	199	428
1	523	391
2	1179	387
3	2665	387
4	5002	387

prune126.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 22.1b

Counts

69 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.3b	(* (atan2 x.im x.re) y.im)
34.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* (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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	307	551
1	925	510
2	2748	491
3	5002	491

prune124.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 3.8b

Counts

83 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
0.1b	(* (log x.re) y.re)
1.3b	(* (atan2 x.im x.re) y.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
24.0ms	(exp (- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im)))
10.0ms	(* (log x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify78.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	258	412
1	840	373
2	2714	349
3	5002	349

prune111.0ms

Filtered

49 candidates to 76 candidates (-55.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 3.8b

Counts

84 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* (atan2 x.im x.re) y.im))
0.5b	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
1.3b	(* (atan2 x.im x.re) y.im)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `add-log-exp`
4×	`sqr-pow`
3×	`div-exp` `associate-r` `associate-l` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

2.0ms	(exp (* (atan2 x.im x.re) y.im))
5.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series43.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(exp (* (atan2 x.im x.re) y.im))
27.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms	(* (atan2 x.im x.re) y.im)

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	266	599
1	1004	563
2	5001	558

prune72.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	82	10	92

Merged error: 3.8b

Counts

92 → 10

regimes458.0ms

Accuracy

67% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 20.3b

bsearch106.0ms

Steps

Iters	Range		Point
11	-1.512366293964845e-287	1.0631385641558184e-306	8.9871369586887e-313

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	2109×	body	1280	valid
842.0ms	7984×	body	80	valid
721.0ms	1559×	body	640	valid
212.0ms	630×	body	320	valid
60.0ms	278×	body	160	valid

Details

sample324.0ms

simplify38.0ms

prune17.0ms

localize31.0ms

rewrite22.0ms

series90.0ms

simplify78.0ms

prune126.0ms

localize16.0ms

rewrite18.0ms

series75.0ms

simplify76.0ms

prune124.0ms

localize11.0ms

rewrite16.0ms

series64.0ms

simplify78.0ms

prune111.0ms

localize10.0ms

rewrite13.0ms

series43.0ms

simplify37.0ms

prune72.0ms

regimes458.0ms

bsearch106.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling