Details

sample53.0ms

Algorithm

intervals

Results

35.0ms

275×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.9b	(+ (* x.re y.re) (* x.im y.im))
26.6b	(/ (+ (* x.re y.re) (* x.im 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`
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))
2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
94.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (31.0ms)

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

prune175.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
15.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x.re y.re) (* x.im y.im))
106.0ms	(/ (+ (* 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)))

simplify81.0ms

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

prune312.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.4b

localize15.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
16.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

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:

2.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
2.0ms	(cbrt (+ (* x.re y.re) (* x.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)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
103.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (115.0ms)

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

prune274.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.4b

localize17.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
30.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
94.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
109.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
92.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	284	506
1	984	470
2	3695	458
3	5002	457

prune259.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.4b

regimes246.0ms

Accuracy

38.2% (1.9b remaining)

Error of 24.7b against oracle of 22.8b and baseline of 25.8b

bsearch5.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	38
1	32	38
2	32	38

end0.0ms

sample856.0ms

Algorithm

intervals

Results

632.0ms

8444×

body

valid