Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

267×

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

prune2.0ms

Filtered

1 candidates to 0 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: 25.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
24.9b	(/ (+ (* 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:

4.0ms	(+ (* 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)))

series134.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
78.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify128.0ms

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

prune163.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 24.6b

Counts

63 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
13.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
120.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune239.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	93	13	106

Merged error: 23.1b

Counts

106 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
13.8b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
18.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
78.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	263	883
1	831	838
2	2287	833
3	5001	833

prune249.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 23.1b

Counts

109 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.7b	(+ (* x.re y.re) (* x.im y.im))
24.3b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* y.re y.re) (* y.im y.im))
49.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
77.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify78.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	393	851
1	2037	747
2	5003	718

prune172.0ms

Filtered

109 candidates to 68 candidates (62.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	109	12	121

Merged error: 23.1b

Counts

121 → 12

regimes232.0ms

Accuracy

0% (2.9b remaining)

Error of 25.8b against oracle of 22.9b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample593.0ms

Algorithm

intervals

Results

367.0ms

8458×

body

valid

Details

sample22.0ms

simplify4.0ms

prune2.0ms

localize12.0ms

rewrite16.0ms

series134.0ms

simplify128.0ms

prune163.0ms

localize12.0ms

rewrite25.0ms

series221.0ms

simplify82.0ms

prune239.0ms

localize15.0ms

rewrite40.0ms

series211.0ms

simplify73.0ms

prune249.0ms

localize10.0ms

rewrite27.0ms

series199.0ms

simplify78.0ms

prune172.0ms

regimes232.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample593.0ms

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