Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

272×

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: 24.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
24.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

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)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune130.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	8	49

Merged error: 24.1b

Counts

49 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(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))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
105.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.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)))

simplify87.0ms

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

prune257.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	94	10	104

Merged error: 22.5b

Counts

104 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

8.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	294	1227
1	871	1172
2	2545	1144
3	5001	1144

prune334.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	111	11	122

Merged error: 22.5b

Counts

122 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-div` `sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

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	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
97.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
93.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify124.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	294	963
1	1015	902
2	4043	887
3	5002	885

prune318.0ms

Filtered

96 candidates to 76 candidates (79.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	93	14	107

Merged error: 22.5b

Counts

107 → 14

regimes290.0ms

Accuracy

0% (3.1b remaining)

Error of 26.0b against oracle of 23.0b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample592.0ms

Algorithm

intervals

Results

371.0ms

8480×

body

valid