Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

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: 25.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
25.1b	(/ (+ (* 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)))

series136.0ms

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))
78.0ms	(/ (+ (* 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 (29.0ms)

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

prune168.0ms

Filtered

62 candidates to 49 candidates (79.0%)

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: 24.8b

Counts

63 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
108.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify87.0ms

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

prune240.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 21.5b

Counts

105 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

13.8b	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))
17.7b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
17.7b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
17.7b	(cbrt (+ (* x.re y.re) (* x.im y.im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-prod`
24×	`associate-/r*`
22×	`cbrt-div`
16×	`add-exp-log`
11×	`flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

18.0ms	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))
100.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
100.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
102.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	560	2242
1	2344	2090
2	5001	1991

prune402.0ms

Filtered

127 candidates to 110 candidates (86.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	126	11	137

Merged error: 21.5b

Counts

137 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

17.7b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
17.7b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
101.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (113.0ms)

Iter	Nodes	Cost
0	254	480
1	655	456
2	1709	444
3	4133	440
4	5001	438

prune224.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	68	11	79

Merged error: 21.5b

Counts

79 → 11

regimes227.0ms

Accuracy

37.5% (1.8b remaining)

Error of 25.0b against oracle of 23.2b and baseline of 26.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	38
1	31	38
2	31	38

end0.0ms

sample507.0ms

Algorithm

intervals

Results

294.0ms

8472×

body

valid