Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

268×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(- (* x.im y.re) (* x.re y.im))
26.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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:

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

series139.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
80.0ms	(/ (- (* 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

prune177.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(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`
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))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* x.im y.re) (* x.re y.im))
106.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

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

prune261.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* x.im y.re) (* x.re y.im))
16.1b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
14.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* x.im y.re) (* x.re y.im))
104.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	378	918
1	1807	831
2	5001	807

prune277.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

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:

6.0ms	(- (* 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))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* x.im y.re) (* x.re y.im))
114.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify95.0ms

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

prune279.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes129.0ms

Accuracy

0% (2.9b remaining)

Error of 26.3b against oracle of 23.4b and baseline of 26.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample481.0ms

Algorithm

intervals

Results

277.0ms

8469×

body

valid