Details

sample328.0ms

Algorithm

intervals

Results

231.0ms	71×	body	1280	valid
30.0ms	259×	body	80	valid
22.0ms	47×	body	640	valid
10.0ms	29×	body	320	valid
2.0ms	11×	body	160	valid

simplify404.0ms

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

prune16.0ms

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: 34.3b

Counts

2 → 1

localize48.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.re)
30.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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:

4.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
61.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (67.0ms)

Iter	Nodes	Cost
0	197	426
1	513	389
2	1157	389
3	2498	389
4	5001	387

prune115.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 20.6b

Counts

69 → 4

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)
1.8b	(* (atan2 x.im x.re) y.im)
30.9b	(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)))

series72.0ms

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))
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)))

simplify77.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (24.0ms)

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

prune112.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Merged error: 3.0b

Counts

82 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (* -1 x.re)) y.re)
1.8b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

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

series39.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
10.0ms	(* (log (* -1 x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

simplify98.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	235	321
1	838	294
2	4203	287
3	5001	287

prune89.0ms

Filtered

37 candidates to 59 candidates (-59.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Merged error: 3.0b

Counts

64 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.re)
30.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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:

4.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (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)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	197	426
1	513	389
2	1157	387
3	2556	387
4	5001	387

prune98.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	68	5	73

Merged error: 3.0b

Counts

73 → 5

regimes395.0ms

Accuracy

80.9% (6.2b remaining)

Error of 9.6b against oracle of 3.5b and baseline of 35.7b

bsearch298.0ms

Steps

Iters	Range		Point
10	6.580860954088717e-166	3.401319575465327e-151	6.710434828305167e-166
9	6.164901767124377e-221	4.0930739739128934e-216	2.0221970332526278e-216
10	-3.069211600425411e-302	4.251265814292649e-304	1.5656916858478e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	35
1	60	35
2	60	35

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2045×	body	1280	valid
846.0ms	7954×	body	80	valid
678.0ms	1459×	body	640	valid
206.0ms	629×	body	320	valid
74.0ms	306×	body	160	valid

Details

sample328.0ms

simplify404.0ms

prune16.0ms

localize48.0ms

rewrite23.0ms

series87.0ms

simplify73.0ms

prune115.0ms

localize16.0ms

rewrite18.0ms

series72.0ms

simplify77.0ms

prune112.0ms

localize12.0ms

rewrite15.0ms

series39.0ms

simplify98.0ms

prune89.0ms

localize25.0ms

rewrite19.0ms

series70.0ms

simplify74.0ms

prune98.0ms

regimes395.0ms

bsearch298.0ms

simplify2.0ms

end0.0ms

sample3.8s

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