Details

sample106.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.21875%

Results

11.0ms

266×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	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: 27.2b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(+ (* x.re y.re) (* x.im y.im))
26.7b	(/ (+ (* x.re y.re) (* x.im 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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

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

series41.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4437	477
3	5002	477

prune105.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 26.4b

Counts

63 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune123.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 25.0b

Counts

105 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune127.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	94	13	107

Merged error: 25.0b

Counts

107 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
1.1b	(+ (* x.re y.re) (* x.im y.im))
26.3b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
28.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
18.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	518	1819
1	2632	1654
2	5001	1567

prune94.0ms

Filtered

84 candidates to 149 candidates (-77.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	148	14	162

Merged error: 25.0b

Counts

162 → 14

regimes527.0ms

Accuracy

26.4% (2.2b remaining)

Error of 25.1b against oracle of 22.9b and baseline of 25.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	20
1	26	20
2	26	20

end0.0ms

sample753.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.21875%

Results

367.0ms

8439×

body

valid

Details

sample106.0ms

simplify4.0ms

prune3.0ms

localize15.0ms

rewrite16.0ms

series41.0ms

simplify130.0ms

prune105.0ms

localize13.0ms

rewrite21.0ms

series58.0ms

simplify82.0ms

prune123.0ms

localize14.0ms

rewrite23.0ms

series55.0ms

simplify82.0ms

prune127.0ms

localize12.0ms

rewrite29.0ms

series62.0ms

simplify69.0ms

prune94.0ms

regimes527.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample753.0ms

Profiling