Details

sample35.0ms

Algorithm

intervals

Results

24.0ms

276×

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: 26.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
26.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(- (* 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)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* 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)))

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

prune175.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

2.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify93.0ms

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

prune280.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
15.8b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
29.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.8b	(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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

2.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	264	887
1	808	842
2	2357	837
3	5001	837

prune300.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
0.8b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite49.0ms

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:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
5.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
40.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
86.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (43.0ms)

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

prune227.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.8b

regimes395.0ms

Accuracy

22.7% (2.4b remaining)

Error of 25.0b against oracle of 22.6b and baseline of 25.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	25
1	21	25

end0.0ms

sample887.0ms

Algorithm

intervals

Results

659.0ms

8445×

body

valid