Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

274×

body

valid

simplify10.0ms

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

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: 24.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
23.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:

4.0ms	(+ (* 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)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune172.0ms

Filtered

64 candidates to 50 candidates (78.1%)

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: 23.4b

Counts

65 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re 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`
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))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.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)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* x.im y.re) (* x.re y.im))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune472.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Merged error: 21.0b

Counts

107 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
0.7b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.4b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite28.0ms

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`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
83.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	384	857
1	1929	753
2	5002	724

prune204.0ms

Filtered

110 candidates to 68 candidates (61.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	110	12	122

Merged error: 21.0b

Counts

122 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
0.5b	(- (* x.im y.re) (* x.re y.im))
23.7b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite31.0ms

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×	`div-exp` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
155.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
35.0ms	(- (* x.im y.re) (* x.re y.im))
56.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	516	1825
1	2545	1663
2	5001	1577

prune232.0ms

Filtered

150 candidates to 83 candidates (55.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	3	6	9
Picked	1	0	1
Done	0	2	2
Total	152	10	162

Merged error: 21.0b

Counts

162 → 10

regimes203.0ms

Accuracy

18.6% (2.5b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 26.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	26
1	27	26
2	27	26

end0.0ms

sample507.0ms

Algorithm

intervals

Results

302.0ms

8450×

body

valid