Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 79.736328%

Results

11.0ms	256×	body	80	valid
1.0ms	17×	body	80	invalid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune3.0ms

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: 26.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(- (* x.im y.re) (* x.re y.im))
25.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series46.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5001	491

prune112.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 25.4b

Counts

65 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3340	845
3	5003	845

prune126.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 22.9b

Counts

107 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

8.5b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 101

Calls

4 calls:

10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	366	1263
1	1122	1192
2	3502	1157
3	5002	1157

prune135.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 22.9b

Counts

124 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify138.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	349	1012
1	1126	951
2	4369	928
3	5002	912

prune95.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	96	13	109

Merged error: 22.9b

Counts

109 → 13

regimes375.0ms

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 25.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 79.736328%

Results

366.0ms	8000×	body	80	valid
26.0ms	498×	body	80	invalid

Details

sample1.4s

simplify9.0ms

prune3.0ms

localize9.0ms

rewrite16.0ms

series46.0ms

simplify40.0ms

prune112.0ms

localize12.0ms

rewrite20.0ms

series57.0ms

simplify101.0ms

prune126.0ms

localize16.0ms

rewrite26.0ms

series93.0ms

simplify101.0ms

prune135.0ms

localize16.0ms

rewrite23.0ms

series85.0ms

simplify138.0ms

prune95.0ms

regimes375.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.9s

Profiling