Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

283×

body

valid

simplify11.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
26.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* y.re y.re) (* y.im y.im))
41.0ms	(- (* x.im y.re) (* x.re y.im))
98.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (30.0ms)

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

prune184.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
17.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite56.0ms

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:

8.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(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 (24.0ms)

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

prune496.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

localize13.0ms

Local error

Found 4 expressions with local error:

11.9b	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
7×	`pow1`
6×	`times-frac` `associate-/r*`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

18.0ms	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	199	562
1	770	521
2	3194	514
3	5001	514

prune250.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.9b

localize18.0ms

Local error

Found 4 expressions with local error:

30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

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:

10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
96.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
98.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1471	416
3	5001	414

prune302.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

regimes156.0ms

Accuracy

0% (1.7b remaining)

Error of 25.3b against oracle of 23.6b and baseline of 25.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	27
1	23	27

end0.0ms

sample565.0ms

Algorithm

intervals

Results

284.0ms

8434×

body

valid