Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	26×	body	320	valid
0.0hr	63×	body	1280	valid
0.0hr	255×	body	80	valid
0.0hr	41×	body	640	valid
0.0hr	15×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0hr)

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

prune0.0hr

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: 34.5b

Counts

2 → 2

localize0.0hr

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite0.0hr

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:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify0.0hr

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 20.8b

Counts

70 → 6

localize0.0hr

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))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite0.0hr

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:

0.0hr	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.0hr	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.0hr	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify0.0hr

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

Filtered

78 candidates to 55 candidates (29.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 3.6b

Counts

84 → 8

localize0.0hr

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite0.0hr

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:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify0.0hr

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 3.6b

Counts

76 → 8

localize0.0hr

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite0.0hr

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:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (atan2 x.im x.re) y.im)
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0hr	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify0.0hr

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	68	8	76

Merged error: 3.6b

Counts

76 → 8

regimes0.0hr

Accuracy

61.9% (6.5b remaining)

Error of 10.0b against oracle of 3.5b and baseline of 20.5b

bsearch0.0hr

Steps

Iters	Range		Point
10	1.6515191358596872e-125	4.795669382585278e-114	8.196049293773377e-119
10	7.911629683117708e-200	7.104566640040457e-182	6.226951751350708e-182
8	7.91242576640244e-304	2.6467534497817823e-299	2.920687254161062e-301
10	-4.485436934755623e-84	-3.0926149035121264e-100	-1.7569389405816738e-92

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	55	44
1	64	44
2	67	44
3	67	44

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	2087×	body	1280	valid
0.0hr	7990×	body	80	valid
0.0hr	1468×	body	640	valid
0.0hr	664×	body	320	valid
0.0hr	320×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling