Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

271×

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: 26.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(+ (* x.re y.re) (* x.im y.im))
26.3b	(/ (+ (* 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)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
77.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune189.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 25.9b

Counts

63 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
16.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x.re y.re) (* x.im y.im))
99.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.0ms	(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	2693	828
3	5001	828

prune286.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 24.4b

Counts

104 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
16.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
100.0ms	(/ (+ (* 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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune242.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 24.4b

Counts

105 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
17.1b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
14.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
99.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	385	911
1	1913	826
2	5002	802

prune213.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 24.4b

Counts

115 → 9

regimes182.0ms

Accuracy

0% (2.9b remaining)

Error of 26.5b against oracle of 23.6b and baseline of 26.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	14
1	22	14

end0.0ms

sample557.0ms

Algorithm

intervals

Results

354.0ms

8431×

body

valid

Details

sample21.0ms

simplify4.0ms

prune2.0ms

localize9.0ms

rewrite16.0ms

series133.0ms

simplify132.0ms

prune189.0ms

localize11.0ms

rewrite21.0ms

series197.0ms

simplify82.0ms

prune286.0ms

localize15.0ms

rewrite21.0ms

series200.0ms

simplify84.0ms

prune242.0ms

localize13.0ms

rewrite29.0ms

series199.0ms

simplify47.0ms

prune213.0ms

regimes182.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample557.0ms

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