Details

sample387.0ms

Algorithm

intervals

Results

56.0ms	77×	body	1280	valid
26.0ms	249×	body	80	valid
21.0ms	44×	body	640	valid
5.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify41.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 35.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.9b	(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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2496	381
4	5001	381

prune293.0ms

Filtered

68 candidates to 54 candidates (79.4%)

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: 18.3b

Counts

69 → 5

localize18.0ms

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)
2.0b	(* (atan2 x.im x.re) y.im)
31.4b	(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)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
91.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	290	540
1	897	500
2	2667	491
3	5002	491

prune229.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 4.0b

Counts

83 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
3.2b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series182.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify103.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	256	510
1	732	441
2	1709	432
3	3785	432
4	5002	432

prune265.0ms

Filtered

82 candidates to 59 candidates (72.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 4.0b

Counts

89 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.0b	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (* -1 x.re)) y.re)
2.0b	(* (atan2 x.im x.re) y.im)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

series259.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
109.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
64.0ms	(* (log (* -1 x.re)) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)

simplify114.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	259	463
1	927	420
2	4704	412
3	5001	412

prune173.0ms

Filtered

77 candidates to 52 candidates (67.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Merged error: 4.0b

Counts

86 → 9

regimes363.0ms

Accuracy

82.3% (5.5b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 34.8b

bsearch103.0ms

Steps

Iters	Range		Point
8	-3.99908892473576e-307	4.5509090925312356e-306	-1.0365888423994e-310

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

sample3.5s

Algorithm

intervals

Results

1.4s	1986×	body	1280	valid
844.0ms	7990×	body	80	valid
670.0ms	1429×	body	640	valid
210.0ms	640×	body	320	valid
60.0ms	279×	body	160	valid