Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

275×

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
28.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

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:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(- (* x.im y.re) (* x.re y.im))
78.0ms	(/ (- (* 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

prune370.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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:

7.0ms	(- (* x.im y.re) (* x.re y.im))
28.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* 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))))
32.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify94.0ms

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

prune646.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.9b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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:

7.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* x.im y.re) (* x.re y.im))
68.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (20.0ms)

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

prune664.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
18.8b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
19.2b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
6×	`times-frac` `associate-/r*`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
71.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* y.re y.re) (* y.im y.im))
111.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	385	746
1	1875	664
2	5001	660

prune486.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.5b

regimes181.0ms

Accuracy

58% (1.1b remaining)

Error of 23.2b against oracle of 22.1b and baseline of 24.7b

bsearch169.0ms

Steps

Iters	Range		Point
8	2.989236853439617e-44	3.1121783822088664e-40	2.9683856602189315e-40
8	-2.0452575119410763e-91	-4.5182054444454834e-95	-9.341981836678716e-94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	28
1	37	28

end0.0ms

sample574.0ms

Algorithm

intervals

Results

364.0ms

8508×

body

valid